SOLUTION: Please help me figure the following problem out. Thank you One leg of a right triangle is 12 cm longer than the other leg. The length of the hypotenuse of the triangle is 36 cm.

Question 90473: Please help me figure the following problem out. Thank you
One leg of a right triangle is 12 cm longer than the other leg. The length of the hypotenuse of the triangle is 36 cm. Find the length of the two legs.
Answer by malakumar_kos@yahoo.com(315) (Show Source): You can put this solution on YOUR website!

One leg of a right triangle is 12 cm longer than the other leg. The length of the hypotenuse of the triangle is 36 cm. Find the length of the two legs.
Let the length of th smaller leg be = x cm

the length of the longer leg = x+12 cm
the length of the hypotenuse = 36 cm
According to Pythagorous theorem , (hypotenuse)^2 = sum of the squares of the other two sides
(hypotenuse)^2 = (smaller leg)^2+ (longer leg)^2
(36)^2 = x^2+ (x+12)^2
1296 = x^2+x^2+24x+144
2x^2+24x+144-1296 = 0
2x^2+24x-1152 = 0
divide by 2 throughout
x^2+12x-576 = 0 since the factors for 576 cannot be found
use the formula x = -b+-sqrtb^2-4ac divided by 2a
we get x = -6+-sqrt 612
the other length is 6+-sqrt 612

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