I need help solving this problem

Question

One leg of a right triangle is 1 centimeters longer than the other leg . The hypotenuse measures 5 centimeters. Find the measure of each leg of the triangle

Answer 1

pythagorean theorem c² = a² + b²

x² + (x + 1)² = 5²

x² + x² + 2x + 1 - 25 = 0

2x² + 2x - 24 = 0

x² + x -12 = 0

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

x = -4 or x = 3

x can't be negative.

One of the leg = 3

The other leg = 3 + 1 = 4

It's a 3-4-5 triangle. One of pythagorean triplets.

Answer 2

Let one leg (say the shorter one) be x. Then how would you represent the longer leg in terms of x?

Since it is a right triangle, you can use the Pythagorean Theorem.

a^2 + b^2 = c^2.

Substitute 5, x, and the expression for the longer leg into the Pythag. Thm. and solve for x.

Then tell the lengths of the two legs.