Rectangles - ACT Math
Card 0 of 351
Two rectangles are similar. The perimeter of the first rectangle is 36. The perimeter of the second is 12. If the base length of the second rectangle is 4, what is the height of the first rectangle?
Two rectangles are similar. The perimeter of the first rectangle is 36. The perimeter of the second is 12. If the base length of the second rectangle is 4, what is the height of the first rectangle?
Solve for the height of the second rectangle.
Perimeter = 2B + 2H
12 = 2(4) + 2H
12 = 8 + 2H
4 = 2H
H = 2
If they are similar, then the base and height are proportionally equal.
B1/H1 = B2/H2
4/2 = B2/H2
2 = B2/H2
B2 = 2H2
Use perimeter equation then solve for H:
Perimeter = 2B + 2H
36 = 2 B2 + 2 H2
36 = 2 (2H2) + 2 H2
36 = 4H2 + 2 H2
36 = 6H2
H2 = 6
Solve for the height of the second rectangle.
Perimeter = 2B + 2H
12 = 2(4) + 2H
12 = 8 + 2H
4 = 2H
H = 2
If they are similar, then the base and height are proportionally equal.
B1/H1 = B2/H2
4/2 = B2/H2
2 = B2/H2
B2 = 2H2
Use perimeter equation then solve for H:
Perimeter = 2B + 2H
36 = 2 B2 + 2 H2
36 = 2 (2H2) + 2 H2
36 = 4H2 + 2 H2
36 = 6H2
H2 = 6
Compare your answer with the correct one above
Two rectangles are similar. The first rectangle has a perimeter of 
and the second has a perimeter of 
. If the first rectangle has a length of 
, what the length of the second rectangle?
Two rectangles are similar. The first rectangle has a perimeter of
1. Create a proportion comparing the two given rectangles:
2. Solve for the length of the second rectangle by cross-multiplying:
1. Create a proportion comparing the two given rectangles:
2. Solve for the length of the second rectangle by cross-multiplying:
Compare your answer with the correct one above
The width of a rectangle is 5 times the length of the rectangle. The width of the rectangle is 30. What is the perimeter of the rectangle?
The width of a rectangle is 5 times the length of the rectangle. The width of the rectangle is 30. What is the perimeter of the rectangle?
If the width is 5 times the length, and the width is 30, then the length is 6. The perimeter of a rectangle is 2 x width + 2 x length. 2 x 30 + 2 x 6 = 72.
If the width is 5 times the length, and the width is 30, then the length is 6. The perimeter of a rectangle is 2 x width + 2 x length. 2 x 30 + 2 x 6 = 72.
Compare your answer with the correct one above
Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:
What is the area of the garden, rounded to the nearest square foot?
Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:
What is the area of the garden, rounded to the nearest square foot?
Perimeter: Sum of the sides:
4x + 4x + 2x+8 +2x+8 = 160
12x + 6 = 160
12x = 154
x = 
Therefore, the short side of the rectangle is going to be:
And the long side is going to be:
The area of the rectangle is going to be as follows:
Area = lw
Perimeter: Sum of the sides:
4x + 4x + 2x+8 +2x+8 = 160
12x + 6 = 160
12x = 154
x =
Therefore, the short side of the rectangle is going to be:
And the long side is going to be:
The area of the rectangle is going to be as follows:
Area = lw
Compare your answer with the correct one above
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
We know that the following represents the formula for the perimeter of a rectangle:
In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:
Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.
We also know that the length is two times the width; therefore, we can write the following:
The area of a rectangle is found by using this formula:
The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.
Compare your answer with the correct one above
A rectangle has a perimeter of 40 inches. It is 3 times as long as it is wide. What is the area of the rectangle in square inches?
A rectangle has a perimeter of 40 inches. It is 3 times as long as it is wide. What is the area of the rectangle in square inches?
The width of the rectangle is w, therefore the length is 3w. The perimeter, P, can then be described as P = w + w + 3w +3w
40 = 8w
w = 5
width = 5, length = 3w = 15
A = 5*15 = 75 square inches
The width of the rectangle is w, therefore the length is 3w. The perimeter, P, can then be described as P = w + w + 3w +3w
40 = 8w
w = 5
width = 5, length = 3w = 15
A = 5*15 = 75 square inches
Compare your answer with the correct one above
Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. If carpet comes in rectangular pieces that measures 5 feet by 4 feet, how many carpet pieces will she need to carpet the entire room?
Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. If carpet comes in rectangular pieces that measures 5 feet by 4 feet, how many carpet pieces will she need to carpet the entire room?
First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.
First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.
Compare your answer with the correct one above
If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?
If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?
the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.
The area of the rectangle can be determined from multiplying length by width, so,
4 x 8 = 32 inches squared
the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.
The area of the rectangle can be determined from multiplying length by width, so,
4 x 8 = 32 inches squared
Compare your answer with the correct one above
If Mrs. Stietz has a patio that measures 96 inches by 72 inches and she wants to cover it with stone tiles that measure one foot by half a foot, what is the minimum number of tiles she needs to cover the patio?
If Mrs. Stietz has a patio that measures 96 inches by 72 inches and she wants to cover it with stone tiles that measure one foot by half a foot, what is the minimum number of tiles she needs to cover the patio?
96. Converting the dimensions of the tiles to inches, they each measure 12 inches by 6 inches. This means that there need to be 8 tiles to span the length of the patio, and 6 tiles to span the width of the patio. She needs to cover the entire area, so we can multiply 8 times 12 to get 96, the number of tiles she needs for the patio.
96. Converting the dimensions of the tiles to inches, they each measure 12 inches by 6 inches. This means that there need to be 8 tiles to span the length of the patio, and 6 tiles to span the width of the patio. She needs to cover the entire area, so we can multiply 8 times 12 to get 96, the number of tiles she needs for the patio.
Compare your answer with the correct one above
The length of a rectangle is 5 times its width. Its width is 3 inches long. What is the area of the rectangle in square inches?
The length of a rectangle is 5 times its width. Its width is 3 inches long. What is the area of the rectangle in square inches?
The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in2.
The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in2.
Compare your answer with the correct one above
A rectangle’s base is twice its height. If the base is 8” long, what is the area of the rectangle?
A rectangle’s base is twice its height. If the base is 8” long, what is the area of the rectangle?
Rectangle
B = 2_H_
B = 8”
H = B/2 = 8/2 = 4”
Area = B x H = 8” X 4” = 32 in2
Rectangle
B = 2_H_
B = 8”
H = B/2 = 8/2 = 4”
Area = B x H = 8” X 4” = 32 in2
Compare your answer with the correct one above
The length of a rectangle is two more than twice the width. The perimeter is 58ft. What is the area of the rectangle?
The length of a rectangle is two more than twice the width. The perimeter is 58ft. What is the area of the rectangle?
For a rectangle, 
and 
, where 
is the length and 
is the width.
Let 
be equal to the width. We know that the length is equal to "two more than twice with width."
The equation to solve for the perimeter becomes 
.
Now that we know the width, we can solve for the length.
Now we can find the area using 
.
For a rectangle,
Let
The equation to solve for the perimeter becomes
Now that we know the width, we can solve for the length.
Now we can find the area using
Compare your answer with the correct one above
The area of a rectangle is 
and its perimeter is 
. What are its dimensions?
The area of a rectangle is
Based on the information given to you, you know that the area could be written as:
Likewise, you know that the perimeter is:
Now, isolate one of the values. For example, based on the second equation, you know:
Dividing everything by 
, you get: 
Now, substitute this into the first equation:
To solve for 
, you need to isolate all of the variables on one side:
or:
Now, factor this:
, meaning that 
could be either 
or 
. These are the dimensions of your rectangle.
You could also get this answer by testing each of your options to see which one works for both the perimeter and the area.
Based on the information given to you, you know that the area could be written as:
Likewise, you know that the perimeter is:
Now, isolate one of the values. For example, based on the second equation, you know:
Dividing everything by
Now, substitute this into the first equation:
To solve for
or:
Now, factor this:
You could also get this answer by testing each of your options to see which one works for both the perimeter and the area.
Compare your answer with the correct one above
A rectangle having a width twice the length of its height has an area of 
. What is the length of its longer side?
A rectangle having a width twice the length of its height has an area of
Since the width is twice the height, we know that the general area equation, which is
could be written:
Thus, we know:
or 
This means that 
must be 
; however, notice that the question asks for the length of the longer side. Thus, the answer is 
.
Since the width is twice the height, we know that the general area equation, which is
could be written:
Thus, we know:
This means that
Compare your answer with the correct one above
What is the area in 
of a yard with dimensions that are 
by 
? (There are 
per 
.)
What is the area in
Because of complexities that arise with square units, it is best to start a problem like this by changing all of your units into inches from the very beginning. Thus, you know that the yard is 
or 
inches by 
or 
inches.
Thus, the area of the yard is 
Because of complexities that arise with square units, it is best to start a problem like this by changing all of your units into inches from the very beginning. Thus, you know that the yard is
Thus, the area of the yard is
Compare your answer with the correct one above
Find the area of a rectangle whose length is 
and width is 
.
Find the area of a rectangle whose length is
To find area, simply multiply length times width. Thus,
To find area, simply multiply length times width. Thus,
Compare your answer with the correct one above
Find the area of a rectangle whose width is 
and length is 
.
Find the area of a rectangle whose width is
To solve, simply multiply width and length. Thus,
To solve, simply multiply width and length. Thus,
Compare your answer with the correct one above
Find the area of rectangle given width of 5 and length of 8.
Find the area of rectangle given width of 5 and length of 8.
To solve, simply use the formula for the area of a rectangle. Thus,
To solve, simply use the formula for the area of a rectangle. Thus,
Compare your answer with the correct one above
A rectangle has a height of 
and a base of 
. What is the length of its diagonal rounded to the nearest tenth?
A rectangle has a height of
1. Use Pythagorean Theorem with 
and 
.
2. Solve for 
, the length of the diagonal:
This rounds down to 
because the hundredth's place (
) is less than 
.
1. Use Pythagorean Theorem with
2. Solve for
This rounds down to
Compare your answer with the correct one above
The sides of rectangle ABCD are 4 in and 13 in.
How long is the diagonal of rectangle ABCD?
The sides of rectangle ABCD are 4 in and 13 in.
How long is the diagonal of rectangle ABCD?
A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:
where a and b are the sides of the rectangle and c is the length of the diagonal.
A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:
Compare your answer with the correct one above