The shortest leg of a triangle is 4 feet shorter than the other leg. the hypotenuse of this triangle is 20 feet. what are the lengths of the two legs of this triangle?

Given:
for example, a and b are the leg of the triangle
a = b - 4
h = 20 ft

Solution:
Use pythagoras theorem to find the solution
a² + b² = h²
(b - 4)² + b² = 20²
b² - 8b + 16 + b² = 400
2b² - 8b +16 - 400 = 0
2b² - 8b - 384 = 0
(each side divided by 2)
b² - 4b - 192 = 0
(b - 16)(b + 12) = 0
b = 16 or b = -12
The length of side can't be negative, so the value of b is 16

Subtitute the value of b to the equation to find a
a = b - 4
a = 16 - 4
a = 12

The lengths of the two legs are 12 ft and 16 ft