SOLUTION: The length of the hypotenuse of a right triangle is 25 dm. Find the lengths of its legs if their sum is 30 cm. Express your answer to the nearest tenth. (Recall the Pythagorean the

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Question 985029: The length of the hypotenuse of a right triangle is 25 dm. Find the lengths of its legs if their sum is 30 cm. Express your answer to the nearest tenth. (Recall the Pythagorean theorem. )
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Interpreting legs as separate from the hypotenuse,
x and y the legs
x%2By=30

y=30-x
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x%5E2%2B%2830-x%29%5E2=25%5E2
x%5E2%2B900-60x%2Bx%5E2-625=0
2x%5E2-60x%2B275=0

Discriminant=3600-4%2A2%2A275=3600-8%2A275=1400
1400=10%2A10%2A14
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sqrt%2810%2A10%2A14%29=10sqrt%2814%29
-

x=%2860%2B-+10sqrt%2814%29%29%2F4

highlight%28x=%2830%2B-+5sqrt%2814%29%29%2F2%29-----either of these is x and the other is y.