The hypotenuse of a triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. What are the lengths of the legs of the triangle?

2 Answers
Mar 20, 2018

The two lengths are 10 feet and 24 feet.

Explanation:

By Pythagoras Theorem, a^2 + b^2 = c^2 .
Since the hypotenuse, c is 26 feet long, 26^2 = 676.
10^2+ 24^2 = 676.
Hence the answer is 10 feet and 24 feet.

Mar 20, 2018

Lengths of the legs are 10 and 24 ft

Explanation:

Let length of one leg of the triangle be x ft , then other leg will

be x+14 ; h= 26 ft . We know h^2 = x^2+ (x+14)^2 or

26^2= x^2+ (x+14)^2 or x^2 +x^2 +28x+196 =676 or

2x^2 +28x-480 =0 or x^2+14x-240=0 or

x^2+24x-10x -240=0 or

x(x+24)-10(x+24)=0 or (x+24)(x-10)=0

Either x+24=0:. x=-24 or x-10=0 :.x=10

leg can not be negative so, x=10 :.x+14=10+14=24

Hence lengths of the legs are 10 and 24 ft . [Ans]