The shortest length of a triangle is 17 feet

Question

The shortest length of a triangle is 17 feet shorter than the other leg. The hypotenuse of this triangle is 25 feet. What are the lengths of the two legs of this triangle

Answer 1

s² + (s - 17)² = 25²

s² + s² - 34s + 289 = 625

2s² - 34s - 336 = 0

s² - 17s - 168 = 0

(s - 24)(s + 7) = 0

 

s - 24 = 0

s = 24

24 - 17 = 7

 

24 feet and 7 feet

 

s + 7 = 0

s = -7

Because we measure using positive numbers, this answer is disregarded.