Using Pythagorean theorem and quadratic equations to determine the length of a right triangle

Question

The hypotenuse of a right triangle Is 5ft long. The shorter leg is 1 ft shorter thang the longer leg. Find the lengths of the triangle

Answer 1

Let x = length of longer leg

Then x-1 = length of shorter leg

By the Pythagorean Theorem, x² + (x-1)² = 25

So, 2x² - 2x - 24 = 0

x² - x - 12 = 0

(x-4)(x+3) = 0

So, x = 4 or x = -3

Since x can't be negative, x = 4 ft and x - 1 = 3 ft