The hypotenuse of a right triangle is 26 feet long one leg of the triangle is 14 feet longer than the other leg find the lengths of the legs of the triangle?

Answer 1

The hypotenuse of a right triangle is 26 feet long one leg of the triangle is 14 feet longer than the other leg find the lengths of the legs of the triangle?

The best advise is to draw a right triangle with the base about twice as long as the height.

Label the height x

Label the base x+14

Label the hypotenuse 26

.

Use Pythagorean Theorem

Eq. #1..(Base)^2 + (Height)^2 = (Hypotenuse)^2

Substitute variables and length of hypotenuse into Eq. #1.

(x)^2 + (x + 14)^2 = (26)^2

x^2 + x^2 +28x + 196 = 676

Combine like terms and move all to the left side.

2x^2 +28x - 480 = 0

This is a quadratic equation. Here is a web site for a quadratic equation solver.

http://www.math.com/students/calculators/source/quadratic.htm

I made a short cut to this site on my desk top, since I use it so often. I solved the quadratic by hand until I found this site. I do not need practice solving quadratic equations by hand.

The 2 answers are 10 and -24. Well, I never saw a triangle with height = -24 feet long.

Height = x = 10 ft.

Base = x + 14 = 24 ft

Check with Pythagorean Theorem

10^2 + 24^2 = 26^2

100 + 576 = 676

We're OK

I find it interesting that though the -24 can not be used, thelong side = +24ft