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 hypotenuse.Math question! Pythagorean theorem

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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!

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial