Question

The perimeter of a rectangle is 220 inches. The ratio of its length to its width is 7:3 Find the area of the rectangle

Answer 1

Given:

Perimeter of rectangle = 220 inches

Ratio of length to width = 7:3

Use the perimeter of a rectangle formula:

P = 2(L + W)

220 = 2(L + W)

Divide both sides by 2:

`\begin{gathered} (220)/(2)=(2(L+W))/(2) \\ \\ 110=L+W \\ \\ \text{Subtract W from both sides:} \\ 110-W=L+W-W \\ \\ 110-W=L \end{gathered}`

Take the ratio:

7W : 3L

7W = 3L

Divide both sides by 3:

`(7)/(3)W=L`

Substitute 7/3 W for L in (110 -W = L)

`\begin{gathered} 110-W=(7)/(3)W \\ \\ \end{gathered}`

Multiply through by 3:

`\begin{gathered} 330-3W=7W \\ \\ 330=7W\text{ + 3W} \\ \\ 330=10W \\ \\ (330)/(10)=W \\ \\ 33=W \end{gathered}`

To find L, we have:

110 - W = L

110 - 33 = L

77 = L

To find the Area, use the formula:

Area = Length x Width

Area = 77 x 33 = 2541 square inches

ANSWER:

2541 square inches