the hypotenuse Of a right triangle is 1 cm longer than the longer leg shorter leg is 17 cm shorter than the longer like find the length of the longer leg of the triangle

Answer 1

Put all sides in terms of the longer leg:

hypotenuse = longer leg (LL) + 1

shorter leg = longer leg (LL) - 17

shorter leg^2 + LL^2 = hypotenuse^2 (Pythagorean Theorem)

(LL - 17)^2 + LL^2 = (LL + 1)^2

LL^2 - 34LL + 289 + LL^2 = LL^2 + 2LL + 1

LL^2 - 34LL +289 = 2LL + 1

LL^2 -36LL + 288 = 0

(LL-24)(LL-12) = 0

LL can't be 12 because shorter leg is 17 less than LL, so LL must be 24

Check:

LL = 24

shorter leg = 7

hypotenuse = 25

verify by Pythagorean Theorem

24^2 + 7^2 = 25^2 ?

625 = 625 check

longer leg is 24 cm