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In a right triangle, one leg is 2 feet less than twice the length of the smaller leg....

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warreh09 | eNotes Newbie

Posted April 28, 2009 at 1:15 AM via web

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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

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cburr | Middle School Teacher | (Level 2) Associate Educator

Posted April 28, 2009 at 7:47 AM (Answer #1)

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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!

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