right triangle

Jan 2008
173
1
The lengths of the sides of a right triangle are consecutive even integers , and the length of the shortest side is a x . which of the following equations could be used to find x ?

(A) x + x + 1 = x + 2
(B) x^2 + (x + 1)^2 = (x + 2)^2
(C) x^2 + (x + 2)^2 = (x + 4)^2
(D) x + x + 2 = x + 4
(E) x^2 = (x + 2)(x + 4)

 
May 2010
1,034
272
the lengths of your sides are:
x
x+2
x+4

The hypoteneuse is the always the longest side, use pythagoras' theorum

If you are completely stuck, read the spoiler
Pythagoras' theorum says \(\displaystyle a^2 + b^2 = c^2\), where c is the hypotenuse.

Apply this as follows:
a = x
b = x+2
c = x+4

\(\displaystyle x^2 + (x+2)^2 = (x+4)^2\)
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
The lengths of the sides of a right triangle are consecutive even integers , and the length of the shortest side is a x . which of the following equations could be used to find x ?

(A) x + x + 1 = x + 2
(B) x^2 + (x + 1)^2 = (x + 2)^2
(C) x^2 + (x + 2)^2 = (x + 4)^2
(D) x + x + 2 = x + 4
(E) x^2 = (x + 2)(x + 4)
If the sides are consecutive even integers, then their lengths are

\(\displaystyle x, x + 2, x+ 4\).


Now what is the extremely well known formula that relates three sides of a right angle triangle?