SOLUTION: The hypotenuse of a right triangle is 34cm. find the length of the two legs, if one leg is 14cm longer than the other. please answer in complete solution

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Question 648002: The hypotenuse of a right triangle is 34cm. find the length of the two legs, if one leg is 14cm longer than the other.
please answer in complete solution
Answer by nerdybill(7384) (Show Source):
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The hypotenuse of a right triangle is 34cm. find the length of the two legs, if one leg is 14cm longer than the other.
.
Let x = short leg
then
x+14 = longer leg
apply Pythagorean theorem, we have:
x^2 + (x+14)^2 = 34^2
x^2 + (x+14)(x+14) = 1156
x^2 + (x^2+28x+196) = 1156
2x^2+28x+196 = 1156
x^2+14x+98 = 578
x^2+14x-480 = 0
(x+16)(x-30) = 0
x = {-16, 30}
we can throw out the negative value (extraneous) leaving:
x = 30 cm (short leg)
.
long leg:
x+14 = 30+14 = 44 cm
.
answer: 30 and 44 cm