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
ron
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.

Binayaka C.
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]

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