A rectangle is drawn so the width is 4 inches longer than the height. If the rectangle's diagonal measurement is 53 inches, find the height.

Question

I dont know how to set it up and I need step by step explanation please!!!

Answer 1

Two unknowns: w and l

You need two equations:

w = l +4

(This makes no sense, because width is always less than length. However, it is how you wrote the problem, so, I'll go with it. Other issue is that a rectangle has no height; it is a two dimensional figure.)

diagonal = 53

Draw a picture. See that you can label the triangle defined by the diagonal (hypotenuse) and the l and the width as follows:

l = l

w = l + 4

hy = 53

So, using P's theorem:

l^2 + (l + 4)^2 = 53^2

l^2 + l^2 + 8l + 16 = 2809

2l^2 + 8l - 2793 = 0

l = 35.42 (ignore negative root)

w = 39.42