Question

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?

Answer 1

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.

Answer 2

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]