SOLUTION: The lengths of the sides of a right traingle whose hypotenuse is 50 ft when its height is 10 ft longer than its base is?

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Question 719036: The lengths of the sides of a right traingle whose hypotenuse is 50 ft when its height is 10 ft longer than its base is?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
h for height, b for base,
h=10+b.
The legs are then b and b+10. Hypotenuse is given, 50.

b%5E2%2B%28b%2B10%29%5E2=50%5E2
b%5E2%2Bb%5E2%2B20b%2B100=2500
2b%5E2%2B20b-2400=0
b%5E2%2B10b-1200=0

The positive radical form should work:
b=%28-10%2Bsqrt%28100-4%2A%28-1200%29%29%29%2F2
b=%28-10%2Bsqrt%284900%29%29%2F2
b=%28-10%2B70%29%2F2
highlight%28b=30%29, the base, so the height must be highlight%2840%29