Length and Width of a Window

Question

A window at Don's house is 24 inches wide and 35 inches tall. He took that window out and replaced it with a larger window that has a perimeter of 472 inches. The new window has the same proportional ratio of width to length as the old window. What is the width and what is the length of the new window?

Answer 1

2(24 + 35) = 118

 

472/118 = 4

 

24(4) = 96"

 

35(4) = 140"

Answer 2

Let w = width of the new window

Let l = length of the new window

 

Because the old and new windows have the same ratio of width to length, we know that 24/35 = w / l

Therefore, l = (35/24)w

 

 

Perimeter = w + w + l + l = 472

 

w + w + (35/24)w + (35/24)w = 472

 

(59/12)w = 472

 

w = 96 inches

 

 

l = (35/24)w = (35/24)*96 = 140 inches