SOLUTION: Suppose that the length of one leg of a right triangle is 3 in more than the length of the other leg. If the length of the hypotenuse is 15 in find the lengths of the two legs.

Question 374096: Suppose that the length of one leg of a right triangle is 3 in more than the length of the other leg. If the length of the hypotenuse is 15 in find the lengths of the two legs.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Suppose that the length of one leg of a right triangle is 3 in more than the
length of the other leg.
If the length of the hypotenuse is 15 in find the lengths of the two legs.
:
Remember a^2 + b^2 = c^2
c is given as 15
let
a = one leg
and
(a+3) = the other leg
:
a^2 + (a+3)^2 = 15^2
:
a^2 + a^2 + 6a + 9 = 225
:
2a^2 + 6a + 9 - 225 = 0; our old friend, the quadratic equation!
:
2a^2 + 6a - 216 = 0
simplify, divide by 2
a^2 + 3a - 108 = 0
factors to
(a-9)(a+12) = 0
the positive solution
a = 9 is one leg
and obviously
12 = the other leg
;
:
Check:
9^2 + 12^2 = 15^2
81 + 144 = 225; confirms our solution
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