SOLUTION: how to find out the length of sides of an rectangle if the diagonal is given 15 cm and the perimeter is given 42 cm

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Question 865836: how to find out the length of sides of an rectangle if the diagonal is given 15 cm and the perimeter is given 42 cm
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y, the sides.

2%28x%2By%29=42 accounts for perimeter.
x%5E2%2By%5E2=15%5E2 accounts for diagonal using Pythagorean Theorem - knowledge about rectangles.

x%2By=21, y=21-x.
x%5E2%2B%2821-x%29%5E2=225
x%5E2%2B21%5E2-42x%2Bx%5E2=225
2x%5E2-42x%2B21%5E2-225=0
2x%5E2-42x%2B216=0
x%5E2-21x%2B108=0
%28x-12%29%28x-9%29=0
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highlight%28x=12%29 or highlight%28x=9%29. Plug these into the formula for y, and find y=9 or y=12.
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DIMENSIONS OF THE RECTANGLE: 9 and 12.