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 meters and the width is 11 meters.

Step-by-step solution

Step 1. Given Information 

• The width of the rectangle is 7 meters less than the length.
• The perimeter of the rectangle is 58 meters.

Step 2. Define the variables

• Let the length of the rectangle is lmeters.
• So, the width will be l -7 meters.

Step 3. Use the formula of Perimeter

• Substitute $P=58,w=l-7$in the formula of perimeter, $P=2w+2l$and solve to find the value of the unknown.

role="math" localid="1644154084896" $$\begin{gathered} 58=2\left(l-7\right)+2\left(l\right) \\ 58=4l-14 \\ 72=4l \\ l=18 \end{gathered}$$

• So, the length of the rectangle is 18 meters.

Step 4. Find the Width

• Substitute $l=18$into $w=l-7$and solve to find the width.

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

• So, the width of the rectangle is 11 meters.

Step 5. Conclusion

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