SOLUTION: The perimeter of a rectangle is 68 cm.If the diagonal is 26cm,find the dimensions of the rectangle.What would the equation be for this?

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Question 1004187: The perimeter of a rectangle is 68 cm.If the diagonal is 26cm,find the dimensions of the rectangle.What would the equation be for this?
Found 2 solutions by Boreal, josgarithmetic:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
L+W=34 (half the perimeter)
L=34-W
Pythagorean theorem
W^2+(34-W)^2=26^2
W^2+W^2-68W+1156=676; 2W^2-68W+480=0
2(W^2-34W+240)=0, factoring 2.
(W-24)(W-10)=0
W=24 or 10. One is length, 24 cm, the other width, 10 cm.
The perimeter is 68 cm.
The square of 24 (576) and 10 (100)= square of diagonal, 26, cm, (676)

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y dimensions, d diagonal.

system%282x%2B2y=68%2Cx%5E2%2By%5E2=d%5E2%29

Let d=26.

system%28x%2By=34%2Cx%5E2%2By%5E2=26%5E2%29

y=34-x
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highlight_green%28x%5E2%2B%2834-x%29%5E2=26%5E2%29--------this can basically be the equation you want. You can simplify it and solve for x, and then use this to solve for y.

x%5E2%2B34%5E2-68x%2Bx%5E2-26%5E2=0
2x%5E2-68x%2B34%5E2-26%5E2=0
2x%5E2-68x%2B%2834%2B26%29%2834-26%29=0
2x%5E2-68x%2B%2860%29%288%29=0
2x%5E2-68x%2B480=0
highlight_green%28x%5E2-34x%2B240=0%29------now simplified, quadratic equation

Discriminant, 34%5E2-4%2A240=196=14%5E2.

x=%2834%2B-+14%29%2F2, which would show BOTH dimensions x AND y.

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Dimensions would be 10 and 24.
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