Question 618436: The hypotenuse of a triangle is 5 feet long the longer of the two legs is one foot longer than the other find the length of the shorter leg Answer by ewatrrr(24785) (Show Source):
Hi,
The hypotenuse of a triangle is 5 feet long
the longer of the two legs is one foot longer than the shorter
Applying the Pythagorean Theorem: legs and
x^2 + (x+1)^2 = 25
x^2 + x^2 + 2x + 1 = 25
2x^2 + 2x - 24 = 0
x^2+x-12 = 0
factoring
(x + 4)(x-3) = 0
x = 3 throwing out negative solution for unit of measure
x = 3ft, the shorter leg. The longer leg is 4ft
AND
3^2 + 4^2 = 5^3
