Applications, Distance, and Midpoint

Question

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?

The length of the shorter leg is : ____ft

The length of the longer leg is _____ft

Answer 1

You would need to use the Pythagorean Theorem and plug in known values.

A² + B² = C²

A = B + 71, B = unknown short side, C = 85

(B + 71)² + B² = 85²

B² + 142B + 5041 + B² = 7225

2B² + 142B = 2184

B² + 71B = 1092

B² + 71B - 1092 = 0

Using quadratic formula, you get B = 13 or B = -84.

So the short side is 13 ft and the other side is 84 ft.

Answer 2

Shorter leg is 33 feet and longer leg is 104 feet.