Finding Length and Width with a Proportion

Question

This is the question in struggling with.

The perimeter of a rectangle is 56 inches. The ratio of the length to the width is 6:1. Find the length an width.

Answer 1

We know that perimeter = 2l + 2w, which could be re-written as: perimeter = 2 (l+w)

The questions states that ratio of length to the width is is 6:1, therefore the length is 6 times greater than the width, which could be written as l= 6w

(if l=6w, then l:w is the same as 6w:w, which is 6:1)

Perimeter = 2(l+w)

If perimeter = 56 inches, length = 6w, and width = w, let's substitute:

56 = 2 (6w +w)

56= 2(7w)

[56/2] = 7w

28 = 7w

4=w

width is 4 inches, and since the length is 6 times the width, length = 6 x 4 = 24 inches

Therefore, width = 4 inches, length = 24 inches

Answer 2

P = 2(l + w)

P/2 = l + w

56/2 = l + w

28 = l + w

If the length is 6 times the width...

28 = 6w + w

28 = 7w

w = 4

l = 6(4)

l = 24

The length is 24 in. and the width is 6 in.

Answer 3

P=2l+2w

half of the perimeter is l+w

the perimeter is 56 so half of that is 28

the ratio of the length to the width is 6:1

6x+x=28

7x=28

x=4

4*6=24 and 4*1=4

the length is 24 inches and the width is 4 inches

l=24 in and w=4 in

check: P=2*24+2*4

P=48+8

P=56 inches, the perimeter of the rectangle