Question

The length of a rectangle is 5 cm more than its width. The perimeter is 82 cm. Find the length of the rectangle.

Answer 1

We will represent the length of the rectangle as $l$ and the width as $w$.

From this problem, we can say $l = w + 5$. We can also deduct an equation from the second sentence:

$2l + 2w = 82$

$2(w + 5) + 2w = 82$ (from substitution)

$2w + 10 + 2w = 82$

$4w = 72$

$\boxed{w = 18}$

Using this value for $w$, we can find $l$:

$l = 18 + 5$

$\boxed{l = 23}$

The length of the rectangle is 23 cm and the width of the rectangle is 18 cm.