# 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...

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### 1 Answer

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- 45X^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+ 8X5X^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!