SOLUTION: The area of a right triangle is 42 square meters. If one leg is 5 meters longer than the other, what are the lengths of the two legs?

Question 225397: The area of a right triangle is 42 square meters. If one leg is 5 meters longer than the other, what are the lengths of the two legs?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Let a,,& b,,,be legs of rt triangle with ,,,,a=b+5
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Area = 1/2 *base* height
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A= 1/2 *a *b,,,,,subst
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A= 1/2 *(b+5) * b
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A = 1/2 (b^2 +5b)
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A=42 = 1/2 (b^2 +5b)
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84 = b^2 +5b
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0= b^2 +5b -84,,,,,,,,factor
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0= (b-7)(b+12)
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b= 7, -12 (not realistic)
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Answer is a=b+5= 7+5=12 m ,,,,,,b= 7m
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check,,,,42 = 1/2 *7 *12 = 42 m^2,,,,ok
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