Question

The length of a rectangle is 5 inches more than the width. The perimeter is 22 inches. Find the length and width

Answer 1

The length of the rectangle is 8 inches and its width is 3 inches.

Step-by-step explanation

Let the length of the rectangle be L.

Let the width of the rectangle be W.

The length of the rectangle is 5 inches more than the width. This implies that:

`L=5+W`

The perimeter of the rectangle is 22 inches. This implies that:

`P=2(L+W)=22`

Substitute the first equation into the second, we have:

`\begin{gathered} 2(5+W+W)=22 \\ \Rightarrow2(5+2W)=22 \\ 10+4W=22 \\ \Rightarrow4W=22-10=12 \\ \Rightarrow W=(12)/(4) \\ W=3in \end{gathered}`

Substitute the value of W into the equation for L:

`\begin{gathered} L=5+3 \\ L=8in \end{gathered}`

Therefore, the length of the rectangle is 8 inches and its width is 3 inches.