Question

The length of a rectangle is 4 centimeters less than twice its width. The perimeter of the rectangle is 34 cm. What are the dimensions of the rectangle?
length = 14 cm; width = 9 cm
length = 10 cm; width=7
length = 7 cm; width = 10 cm
length = 9 cm; width = 8 cm

Answer 1

Let l and w be the length and width of the rectangle. We know that $l=2w-4$

The formula for the perimeter is $P=2(w+l)$

Using our substitution, it becomes

$P=2(w+2w-4)=2(3w-4)=6w-8$

We know that the perimeter is 34, so we have

$6w-8=34 \iff 6w=42 \iff w=7$

The length is 4 less than twice the width, so we have

$l=2\cdot 7 - 4 = 10$