Rhonda M.

asked • 05/16/19# Measurements of a right triangle

One leg of a right triangle is four inches longer than the other. The hypotenuse is 20 inches. Whatever are the measurements of the triangle?

## 1 Expert Answer

x = one leg

x + 4 = other leg

(x + 4)^{2} + x^{2} = 20^{2} Pythagorean's theorem a^{2} + b^{2} = c^{2}

x^{2} + 8x + 16 + x^{2 }= 400

2x^{2} + 8x - 384 = 0 Subtract 400 from both sides of the equation

2(x^{2} + 4x - 192) = 0 Factor two from everything

Using __the quadratic equation__ you get the results **x =−16** and** x = 12**.

Since the legs of the right triangle cannot be negative x = 12 is the answer we use along with 12 + 4 = 16.

The legs of the right triangle are **12 and 16** with a hypotenuse of 20.

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Rhonda M.

Thank you!05/16/19