Question

The length of the rectangle is 1/4th the width of the rectangle. The perimeter is 35 ft. How long is the length and width?

Answer 1

Perimeter= 2l + 2w
Perimeter= 35ft
l= 1/4w

Substitute values above for l and w

35= 2(1/4w) + 2w
35= (2*1)/4w + 2w
35= 2/4w + 2w
35= 1/2w + 2w
35= 2 1/2w
convert to improper fraction
35= 5/2w
divide both sides by 5/2
35 ÷ 5/2= w
multiply by reciprocal of 5/2
35 * 2/5= w
(35*2)/5= w
70/5= w
14= w

Substitute 14=w to find l

l= 1/4w
l= 1/4(14)
l= (1*14)/4
l= 14/4
reduce/simplify by 2
l= 7/2 or 3 1/2

CHECK:
35= 2l + 2w
35= 2(7/2) + 2(14)
35= 7 + 28
35= 35

ANSWER: l= 7/2 or 3 1/2; w= 14

Hope this helps! :)

Answer 2

---- x ----
|            | 0.25x
---- x ----


x + x + 0.25x + 0.25x = 35
2.5x = 35
x = 35/2.5
x = 14
width is 14

length is 1/4 this.
length = 7/2