SOLUTION: 1. The length of one leg of a right triangle is 6 cm more than the other. If the length of the hypotenuse is 18 cm, what are the lengths of the two legs? Please give the answer in

Question 93459: 1. The length of one leg of a right triangle is 6 cm more than the other. If the length of the hypotenuse is 18 cm, what are the lengths of the two legs? Please give the answer in ascending order rounded to the nearest tenth of a cm.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let x=leg #1, y=leg #2

Since the length of one leg of a right triangle is 6 cm more than the other, this means we can write

Now lets use Pythagorean's theorem to set up the problem

Plug in the hypotenuse h=18 and y=x+6

Foil

Square 18

Subtract 324 from both sides

Combine like terms

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=12, and c=-288

Square 12 to get 144

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our possible solutions are:
or

Since a negative length doesn't make sense, our only solution is

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Check:

First find y

Now plug in the triangle's dimensions

Simplify. Since we rounded, this is as close as it gets. So our answer is verified.
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