ISEE Lower Level Math : How to find the perimeter of a rectangle

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #71 : Plane Geometry

Dennis is building a fence around his field to keep his cattle from getting off the property. If Dennis’ field is \(\displaystyle \small 3\) miles long and \(\displaystyle \small 2\) miles wide, how much fence will Dennis need to surround all of his property?

Possible Answers:

\(\displaystyle 10\ mi\)

\(\displaystyle 12\ mi\)

\(\displaystyle 5\ mi\)

\(\displaystyle 6\ mi\)

\(\displaystyle 7\ mi\)

Correct answer:

\(\displaystyle 10\ mi\)

Explanation:

In order to determine how much fence Dennis will need, we must find the perimeter of his property, which can be found using the formula \(\displaystyle \small \small 2W+ 2L\). When we plug \(\displaystyle \small 2\ mi\) in the \(\displaystyle \small W\) and \(\displaystyle \small 3\ mi\) in for \(\displaystyle \small L\), we find that Dennis needs \(\displaystyle \small 10\ mi\) of fence to surround his property.

\(\displaystyle \small 2(2\ mi) + 2(3\ mi) = 10\ mi\)

 

 

 

 

 

 

Example Question #1 : How To Find The Perimeter Of A Rectangle

Rectangle

Give the perimeter of the rectangle in the above diagram.

Possible Answers:

\(\displaystyle 29\textrm{ in}\)

\(\displaystyle 99\textrm{ in}\)

\(\displaystyle 116\textrm{ in}\)

\(\displaystyle 198\textrm{ in}\)

\(\displaystyle 58\textrm{ in}\)

Correct answer:

\(\displaystyle 58\textrm{ in}\)

Explanation:

Add the length and the height, then multiply the sum by two:

\(\displaystyle (11 + 18) \times 2 = 29 \times 2 = 58\)

The rectangle has a perimeter of 58 inches.

Example Question #2 : How To Find The Perimeter Of A Rectangle

Rectangle

Give the perimeter of the above rectangle in feet.

Possible Answers:

\(\displaystyle 7 5\textrm{ ft}\)

\(\displaystyle 7 \frac{1}{2} \textrm{ ft}\)

\(\displaystyle 37 \frac{1}{2} \textrm{ ft}\)

\(\displaystyle 3 \frac{3}{4} \textrm{ ft}\)

\(\displaystyle 8\textrm{ ft}\)

Correct answer:

\(\displaystyle 7 \frac{1}{2} \textrm{ ft}\)

Explanation:

Use the following formula, substituting \(\displaystyle L = 30, W = 15\) :

\(\displaystyle A = 2 (L + W)\)

\(\displaystyle A = 2 (30 + 15) = 2 \times 45 = 90 \textrm{ in}\)

Now, divide this by 12 to convert inches to feet.

\(\displaystyle \frac{90}{12} = 7 \textrm{ R }6\)

6 inches make half of a foot, so this means the perimeter is \(\displaystyle 7 \frac{1}{2}\) feet.

Example Question #91 : Geometry

What is the perimeter of a rectangle that has a length of \(\displaystyle \small 7\) inches and a width of \(\displaystyle \small 4\) inches? \(\displaystyle \small \left ( P=2l+2w\right )\)

Possible Answers:

\(\displaystyle \small 11\)

\(\displaystyle \small 22\)

\(\displaystyle \small 26\)

\(\displaystyle \small 28\)

Correct answer:

\(\displaystyle \small 22\)

Explanation:

The perimeter of a shape is the sum of all its sides. To find the perimeter of a rectangle, one can use the formula listed above, \(\displaystyle \small \left ( P= 2l+2w\right )\), since a rectangle has opposite sides of equal length.

The length of the rectangle is \(\displaystyle \small 7\):

\(\displaystyle \small 2\times7=14\)

The width of the rectangle is \(\displaystyle \small 4\):

\(\displaystyle \small 4\times2=8\).

\(\displaystyle \small 14+8=22\)

Therefore, the perimeter is \(\displaystyle \small 22\).  

Example Question #92 : Geometry

What is the perimeter of a rectangle with length equal to 5 and width equal to 3?

Possible Answers:

16

8

15

30

Correct answer:

16

Explanation:

\(\displaystyle P=2(l+w)=2(5+3)=2(8)=16\)

Example Question #1 : How To Find The Perimeter Of A Rectangle

What is the perimeter of a rectangle with a width of \(\displaystyle 5\) and a length of \(\displaystyle 8\)?

Possible Answers:

\(\displaystyle 30\)

\(\displaystyle 26\)

\(\displaystyle 13\)

\(\displaystyle 40\)

Correct answer:

\(\displaystyle 26\)

Explanation:

The perimeter of a rectangle is equal to the sum of all its sides. The formula for finding the perimeter of a rectangle is \(\displaystyle P= 2(l+w)\)

The length of the rectangle is eight, and the width is five; \(\displaystyle 8+5=13\).

\(\displaystyle 13\times2=26\)

Therefore, the perimeter of the rectangle is \(\displaystyle 26\).

Example Question #4 : How To Find The Perimeter Of A Rectangle

Mr. Barker is building a rectangular fence. His yard has an area of \(\displaystyle 24\) feet, and the one side of the fence he's already built is \(\displaystyle 6\) feet long. 

What will the perimeter of his fence be when he is finished building it?

Possible Answers:

\(\displaystyle 18\ feet\)

\(\displaystyle 20\ feet\)

\(\displaystyle 36\ feet\)

\(\displaystyle 24\ feet\)

\(\displaystyle 14\ feet\)

Correct answer:

\(\displaystyle 20\ feet\)

Explanation:

The perimeter is calculated by adding up all the sides of the rectangle—in this case,

\(\displaystyle 6+6+4+4=20\)

So the perimeter is \(\displaystyle 20\) feet.

Example Question #1 : How To Find The Perimeter Of A Rectangle

A rectangle has sides 10 cm and 4 cm. What is its perimeter?

Possible Answers:

\(\displaystyle 28\ cm\)

\(\displaystyle 14\ cm\)

\(\displaystyle 40\ cm\)

\(\displaystyle 16\ cm\)

\(\displaystyle 20\ cm\)

Correct answer:

\(\displaystyle 28\ cm\)

Explanation:

A rectangle has two sides of congruent, or equal, sides. Therefore, there are two 10 cm sides and two 4 cm sides. Perimeters is the sum of all the sides, so you must add up the four sides. The answer is 28 cm.

Example Question #71 : Rectangles

If a rectangle has a width of 6.5 inches and a length of 9 inches, what is its perimeter?

Possible Answers:

\(\displaystyle 30\)

\(\displaystyle 33\)

\(\displaystyle 26\)

\(\displaystyle 29\)

\(\displaystyle 31\)

Correct answer:

\(\displaystyle 31\)

Explanation:

The perimeter of a rectangle is found by adding together all four sides. Two sides will be equal to the length, and two sides will be equal to the width.

\(\displaystyle P=width+width+length+length\)

\(\displaystyle P=2l+2w\)

Since the width is 6.5 inches and the length is 9 inches, the perimeter would be:

\(\displaystyle P=6.5+6.5+9+9\)

\(\displaystyle P=2(6.5)+2(9)\)

\(\displaystyle P=13+18\)

\(\displaystyle P=31\)

Example Question #2 : How To Find The Perimeter Of A Rectangle

If Margaret is buying a tablecloth for a table that is 4 feet by 2 feet, what should be the area of the tablecloth?

Possible Answers:

\(\displaystyle 6\ \text{ft}^2\)

\(\displaystyle 8\ \text{ft}^2\)

\(\displaystyle 16\ \text{ft}^2\)

\(\displaystyle 12\ \text{ft}^2\)

\(\displaystyle 22\ \text{ft}^2\)

Correct answer:

\(\displaystyle 8\ \text{ft}^2\)

Explanation:

We will need to find the area of the rectangle by multiplying the length by the width:

\(\displaystyle A=l\times w\)

Use the given dimensions:

\(\displaystyle A=4\times2=8\ \text{ft}^2\)

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