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.

Click here to see ALL problems on Pythagorean-theorem

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