SOLUTION: A rectangle is drawn so the width is 97 inches longer than the height. If the rectangle's diagonal measurement is 113 inches, find the height.

Question 1042388: A rectangle is drawn so the width is 97 inches longer than the height. If the rectangle's diagonal measurement is 113 inches, find the height.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangle is drawn so the width is 97 inches longer than the height.
x = the height
the
(x+97) = the width
If the rectangle's diagonal measurement is 113 inches, find the height.
The diagonal is the hypotenuse, use Pythagoras to find the height
x^2 + (x+97)^2 = 113^2
x^2 + x^2 + 194x + 9409 = 12769
2x^2 + 194x + 9409 - 12769 = 0
2x^2 + 194x - 3360 = 0
simplify divide by 2
x^2 + 97x - 1680 = 0
You can use the quadratic formula a=1; b=97; c=-1680, but this will factor to
(x+112)(x-15) = 0
The positive solution is what we want here
x = 15 inches is the height
:
:
:
See if that checks out, the width: 15+97 = 112, find the hypotenuse with these values
h = in your calc
h = 113
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