Question 17860: A right triangle has side lengths that are consecutive even integers. Use the pythagorean theorem to find the lengths of those sides. Please help!
Answer by whisper(27)   (Show Source):
You can put this solution on YOUR website! Let's start by representing the three sides of the triangle:
x
x+1
x+2
Now let's look at the Pythagorean Theorem:
a^2+b^2=c^2 where a,b are sides of a right triangle and c is the hypoteneuse.
Now we set up the equation:
x^2+(x+1)^2=(x+2)^2
x^2+x^2+2x+1=x^2+4x+4
2x^2+2x+1=x^2+4x+4
Now let's get everything on one side of the equation:
2x^2-x^2+2x-4x+1-4=x^2-x^2+4x-4x+4-4
x^2-2x-3=0
Factor:
(x-3)(x+1)=0
x-3=0 or x+1=0
x=3 lr x = -2
x cannot be negative therefore x =3
If x=3 then
x+1=4
x+2=5
and you have a 3,4,5 triangle.
please don't hesitate to ask if you have further questions!
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