SOLUTION: The perimeter of a rectangle is 26 and its diagonal is √97. Find its length and width. I need help setting this up. Thank you in advance.

Algebra ->  Rectangles -> SOLUTION: The perimeter of a rectangle is 26 and its diagonal is √97. Find its length and width. I need help setting this up. Thank you in advance.      Log On


   

Question 963991: The perimeter of a rectangle is 26 and its diagonal is √97. Find its length and width.
I need help setting this up. Thank you in advance.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x and y, the dimensions.
2x%2B2y=26, for perimeter information.
This simplifies to x%2By=13.


Diagonal, sqrt%2897%29=sqrt%28x%5E2%2By%5E2%29.

Square both sides, 97=x%5E2%2By%5E2
and make a substitution for either variable.
y=13-x
-
x%5E2%2B%2813-x%29%5E2=97
x%5E2%2B169-26x%2Bx%5E2-97=0
2x%5E2-26x%2B169-97=0
2x%5E2-26x%2B72=0
x%5E2-13x%2B36=0
highlight_green%28%28x-4%29%28x-9%29=0%29

Since either x or y could stand for either dimension, the two dimensions' sizes
are 4 and 9.