Question

The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.

Short answer

The length of the rectangle is 18 and the width of the rectangle is 11.

Step-by-step solution

Step 1. Given information

Let the length of the rectangle be x

and the width of the rectangle is $x-7$.

The perimeter of the rectangle is 58.

Step 2. Use the formula for the perimeter of the rectangle.

The perimeter of a rectangle is $P=2(l+w)$.

Substitute the values.

$$\begin{gathered} 58=2(x+x-7) \\ \frac{58}{2}=2x-7 \\ 29=2x-7 \\ 29+7=2x \\ 36=2x \\ \frac{36}{2}=x \\ x=18 \end{gathered}$$

Step 3. Find the length and breadth of the rectangle.

The width of the rectangle is,

$$\begin{gathered} w=x-7 \\ =18-7 \\ =11 \end{gathered}$$

The length of the rectangle is 18 and the width is 11.