In a right triangle, one leg is 2 feet less than twice the length of the smaller leg. The hypotenuse is 2 feet more than twice the length of the smaller leg. Determine the length of the...
You need the pythagorean theorem to solve this, but you also need to know how to multiply binomials.
The short leg is X, the longer leg is (2X - 2) and the hypotenuse is (2X + 2).
We know the pythagorean theorem:
leg^2 + leg^2 = hypotenuse^2
So, in this case:
X^2 + (2X - 2)^2 = (2X + 2)^2
The next step is to expand the binomials. Take each part of the first one and multiply it against each part of the second one.
(2X - 2)(2X - 2) = 4X^2 - 4X - 4X + 4
= 4X^2 - 8X + 4
Then on the other side:
(2X + 2)(2X + 2) = 4X^2 + 4X + 4X + 4
= 4X^2 + 8X + 4
String it all together, and you get this:
X^2 + 4X^2 - 8X + 4 = 4X^2 + 8X + 4
You can combine the first two elements on the left, to get:
5X^2 - 8X + 4 = 4X^2 + 8X + 4
Now you just need to simplify this. First, subtract 4 from each side. That leaves you with:
5X^2 - 8X + 4 - 4 = 4X^2 + 8X + 4 - 4
5X^2 - 8X = 4X^2 + 8X
Next, get rid of the -8X on the left by adding 8X to each side.
5X^2 - 8X + 8X = 4X^2 + 8X + 8X
5X^2 = 4X^2 + 16X
You should see the process by now. I think you can finish simplifying this equation. Start by subtracting 4X^2 from each side!!! Good luck!