Question 873923: I need to find X in a 90 degree triangle with sides X, X+7, and 13. The hypotenuse is the side with 13.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! I need to find X in a 90 degree triangle with sides X, X+7, and 13. The hypotenuse is the side with 13.
Because one angle of the triangle is 90 degrees, you have a "right triangle". Since it is a right triangle, you can apply Pythagorean theorem:
a^2 + b^2 = c^2
where
a, b are the legs
and
c is the hypotenuse
.
x^2 + (x+7)^2 = 13^2
x^2 + x^2+14x+49 = 169
2x^2+14x+49 =169
2x^2+14x-120 = 0
x^2+7x-60 = 0
(x+12)(x-5) = 0
x = {-12, 5}
throw out the negative solution (extraneous) leaving
x = 5
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