Question

One side of a rectangle is 7 inches shorter than five times another side. Find the length of the longer side if we also know that the perimeter of the rectangle is 142 inches.

Answer 1

58 inches

Explanation:

Let the length of the other side = y

One side of a rectangle is 7 inches shorter than five times another side.

• Therefore, the length of the other side = 5y-7

Given that the perimeter of the rectangle is 142 inches.

`\begin{gathered} \text{Perimeter}=2(\text{Length}+\text{WIdth)} \\ \implies142=2(5y-7+y)_{} \end{gathered}`

Next, solve for y.

`\begin{gathered} \text{Divide both sides by 2} \\ (142)/(2)=6y-7 \\ 71=6y-7 \\ \text{Add 7 to both sides.} \\ 71_{}+7=6y-7+7 \\ 78=6y \\ \text{Divide both sides ny 6} \\ (6y)/(6)=(78)/(6) \\ y=13\text{ inches} \end{gathered}`

Next, we find the other side length.

`5y-7=5(13)-7=65-7=58\text{ inches}`

The length of the longer side is 58 inches,