SOLUTION: The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (length and width) of the rectangle? Thanks in advance

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (length and width) of the rectangle? Thanks in advance      Log On


   

Question 119202: The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (length and width) of the rectangle?
Thanks in advance!
Jessica
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The length is 1 cm longer than the width, so if the width is w, the length is w +1. The diagonal of the rectangle forms a right triangle with the length and the width, so Pythagoras says:

w%5E2%2B%28w%2B1%29%5E2=4%5E2

Expand the binomial and collect terms:

w%5E2%2Bw%5E2%2B2w%2B1=16

2w%5E2%2B2w%2B1-16=0

2w%5E2%2B2w-15=0

Use the quadratic formula:

w+=+%28-2+%2B-+sqrt%28+4-4%2A2%2A%28-15%29+%29%29%2F%284%29+

w=%28-2%2B-sqrt%28124%29%29%2F4

w=%28-1%2B-sqrt%2831%29%29%2F2

w=%28-1-sqrt%2831%29%29%2F2%3C0 so this won't do as an answer because a rectangle can't have a negative width. So, w=%28-1%2Bsqrt%2831%29%29%2F2 is the width.

is then the length.