# The hypotenuse of a right triangle is 10 inches. The lengths of the two legs are given by 2 consecutive even integers. How do you find the lengths of the two legs?

##### 1 Answer

Jan 4, 2016

#### Explanation:

The first thing to tackle here is how to express "two consecutive even integers" algebraically.

Apply the Pythagorean theorem:

#(2x)^2+(2x+2)^2=10^2#

#4x^2+4x^2+8x+4=100#

#8x^2+8x-96=0#

#x^2+x-12=0#

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

#x=-4,3#

Thus,

The legs are

#2xrArr6#

#2x+2rArr8#

#"hypotenuse"rArr10#

A more intuitive way to do this problem is to recognize that a