The hypotenuse of a right triangle is seventeen feet. one leg is one foot shorter than twice the length of the other leg. what are the lengths of the legs?

Answer 1

Your right triangle has lengths of x, 2x-1 and hypotenuse of 17.

Using Pythagorean Theorem,

x² + (2x-1)² = 17²

x² + (2x-1)(2x-1)=289

x²+4x²-4x+1=289

5x²-4x+1-289=0

5x²-4x-288=0

Using AC method Multiply 5 times -288=-1440

-40 x 36 = -1440

5x^2-40x+36x-288=0

Factor by grouping

5x(x-8)+36(x-8)=0

(5x+36)(x-8)=0

Set each equal to zero

5x+36=0

x=36/5=-7.2 extraneous cannot have a negative side

x-8=0

x=8

2x-1=2(8)-1=15

So the legs are 8 and 15

To check:

8²+15²=17²

64+225=289

289=289 checks