SOLUTION: The diagonal of a rectangle is 25 inches more than its width. The length of the rectangle is 23 inches more than its width. What is the width of the rectangle?

Question 135546: The diagonal of a rectangle is 25 inches more than its width. The length of the rectangle is 23 inches more than its width. What is the width of the rectangle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The diagonal of a rectangle is 25 inches more than its width. The length of the rectangle is 23 inches more than its width. What is the width of the rectangle?
:
Use pythag: a^2 + b^2 = c^2
:
Let b = width
then
a = (b+23)
and
c = (b+25)
:
(b+23)^2 + b^2 = (b+25)^2
FOIL
b^2 + 46b + 529 + b^2 = b^2 + 50b + 625
Combine like terms on the left
b^2 + b^2 - b^2 + 46b - 50b + 529 - 625 = 0
:
b^2 - 4b - 96 = 0
Factor
(b-12)(b+8) = 0
:
b = +12 inches is the width
then
12 + 23 = 35 inches is the length
and
12 + 25 = 37 inches is the diagonal:
:
:
Check solution:
=
=
= 37
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