SOLUTION: one leg of a triangle is 7 ft longer than other leg. The length of the hypothenuse is 13ft. Find the lengths of the other two sides. How would I set this up? I know its a� + b�

Question 428650: one leg of a triangle is 7 ft longer than other leg. The length of the hypothenuse is 13ft. Find the lengths of the other two sides.
How would I set this up? I know its a� + b� = c� but I don't know which is which or how to go about setting it up to solve.
Found 2 solutions by ewatrrr, Gogonati:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi
one leg of a triangle is 7 ft longer than other leg
Let x and (x+7)represent th elengths of the two legs respectively
a� + b� = c�
x^2 + (x+7)^2 = 13^2
2x^2 + 14x -120 = 0
x^2 + 7x - 60 = 0
(x + 12)(x-5) = 0
(x + 12)=0 x = 12 |tossing out negative solution for length
(x-5) = 0
x = 5, the other side is 12 (5+7)
CHECKING our Answer***
25 + 144 = 169 = 13^2
Answer by Gogonati(855) (Show Source): You can put this solution on YOUR website!
Let x ft the length of one leg. Then the other leg will be: x+7 ft. Since the hypotenuse is 13 ft, we write the Pythagorean theorem:

, Set the equation to zero.
, divide both sides by 2
, factor the equation.
(x-5)(x+12)=0 => x-5=0 => x=5 and x+12=0 => x=-12 Since the length is always positive, the root -12 is rejected.
Answer: The short leg is 5 ft and the long one is 5+7=12 ft.
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