The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in².

Rectangle

B = 2H

B = 8”

H = B/2 = 8/2 = 4”

Area = B x H = 8” X 4” = 32 in²

For a rectangle, \(\displaystyle P = 2l + 2w\) and \(\displaystyle A = lw\), where \(\displaystyle l\) is the length and \(\displaystyle w\) is the width.

Let \(\displaystyle w\) be equal to the width. We know that the length is equal to "two more than twice with width."

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

The equation to solve for the perimeter becomes \(\displaystyle 58 = 2(2w + 2) + 2w\).

\(\displaystyle 58 = 4w + 4+2w=6w+4\)

\(\displaystyle 54=6w\)

\(\displaystyle 9=w\)

Now that we know the width, we can solve for the length.

\(\displaystyle l=2w + 2 = 20\)

Now we can find the area using \(\displaystyle A = lw\).

\(\displaystyle A=(20ft)(9ft)=180ft^2\)

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

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.

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

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.

Perimeter:  Sum of the sides:

4x + 4x + 2x+8 +2x+8 = 160

12x + 6 = 160

12x = 154

x = \(\displaystyle \frac{77}{6}\)

Therefore, the short side of the rectangle is going to be:

 \(\displaystyle \dpi{100} \dpi{100} 2\cdot \frac{77}{6}+3=\frac{172}{6}=\frac{86}{3}\)

And the long side is going to be:

\(\displaystyle \dpi{100} 4\cdot \frac{77}{6}=\frac{308}{6}=\frac{154}{3}\)

The area of the rectangle is going to be as follows:

Area = lw

\(\displaystyle \dpi{100} Area = \frac{86}{3}\cdot \frac{154}{3}=\frac{13,244}{9}=1471.55\approx 1472\ ft^{2}\)

Based on the information given to you, you know that the area could be written as:

\(\displaystyle wl=80\)

Likewise, you know that the perimeter is:

\(\displaystyle 2w+2l=36\)

Now, isolate one of the values. For example, based on the second equation, you know:

\(\displaystyle 2w=36-2l\)

Dividing everything by \(\displaystyle 2\), you get: \(\displaystyle w=18-l\)

Now, substitute this into the first equation:

\(\displaystyle (18-l)l=80\)

To solve for \(\displaystyle l\), you need to isolate all of the variables on one side:

\(\displaystyle 18l-l^2=80\)

or:

\(\displaystyle l^2-18l+80=0\)

Now, factor this:

\(\displaystyle (l-8)(l-10)=0\), meaning that \(\displaystyle l\) could be either \(\displaystyle 8\) or \(\displaystyle 10\). 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.

Since the width is twice the height, we know that the general area equation, which is

\(\displaystyle A=wh\)

could be written:

\(\displaystyle A = 2h*h\)

Thus, we know:

\(\displaystyle 2h^2 = 450\) or \(\displaystyle h^2=225\)

This means that \(\displaystyle h\) must be \(\displaystyle 15\); however, notice that the question asks for the length of the longer side. Thus, the answer is \(\displaystyle 30\).