SOLUTION: Please help me solve this question. The length of the shorter leg, A, of a right triangle is 6 centimeters less than the length of the hypotenuse, C, and the length of the longer l

Question 627470: Please help me solve this question. The length of the shorter leg, A, of a right triangle is 6 centimeters less than the length of the hypotenuse, C, and the length of the longer leg, B, is 3 centimeters less than the length of the hypotenuse. Find the length of the sides of the right triangle.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Please help me solve this question. The length of the shorter leg, A, of a right triangle is 6 centimeters less than the length of the hypotenuse, C, and the length of the longer leg, B, is 3 centimeters less than the length of the hypotenuse. Find the length of the sides of the right triangle.
.
Let h = length of hypotenuse
then
h-6 = length of shorter leg a
h-3 = length of longer leg b
.
applying Pythagorean theorem:
(h-6)^2 + (h-3)^2 = h^2
(h-6)(h-6) + (h-3)(h-3) = h^2
(h^2-12h+36) + (h^2-6h+9) = h^2
2h^2-18h+45 = h^2
h^2-18h+45 = 0
(h-3)(h-15) = 0
h = {3, 15}
the 3 is extraneous, throw it out leaving:
h = 15 centimeters (hypotenuse)
.
shorter leg a:
h-6 = 15-6 = 9 centimeters
.
longer leg b:
h-3 = 15-3 = 12 centimeters
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