The long leg of a right triangle is 71 feet longer than the short leg. The hypotenuse is 85 feet long. How long are the legs of the right triangle?

Question

The length of the shorter leg is

The length of the longer leg is

Answer 1

You have 2 unknowns, so you need 2 equations. Let's use X and Y for the 2 unknown sides:

Because you have a right triangle, and you know the hypotenuse, you can use the Pythagorean Theorem:

x² + y² = 85²

You are told the difference between the 2 sides:

x = y + 71

Now you have 2 equations. Use the expression for x in the 2nd equation, and substitute into the first:

(y + 71)² + y² = 85²

^{Expand this, simplify, and put in standard form. Then you will be able to solve it using the standard methods for quadratics.}

Answer 2

Draw and label a diagram.

s represents the length of the short leg

s + 71 represents the length of the long leg

s² + (s + 71)² = 85²

Can you solve for s and answer?