Question 305294: Please solve.
One leg of a right triangle is four less than twice the other.
The hypotenuse is 10. Find the length of each leg. Answer by nerdybill(7384) (Show Source):
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One leg of a right triangle is four less than twice the other.
The hypotenuse is 10. Find the length of each leg.
.
Let x = one leg
then
2x-4 = other leg
.
Applying Pythagorean theorem:
x^2 + (2x-4)^2 = 10^2
x^2 + (2x-4)(2x-4) = 100
x^2 + 4x^2-8x-8x+16 = 100
5x^2-16x+16 = 100
5x^2-16x-84 = 0
5x^2-30x+14x-84 = 0
(5x^2-30x)+(14x-84) = 0
5x(x-6)+14(x-6) = 0
(x-6)(5x+14) = 0
x = {-14/5, 6}
Toss out the negative answer leaving:
x = 6
