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