SOLUTION: the hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle

Question 212135: the hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle

Step 1. Let x be length of one of the legs. Then x+6 is the length of the other leg. And length of hypotenuse is 2x.

Step 2. Pythagorean Theorem. Sum of the squares of the legs is equal to the square of the hypotenuse.

Simplify right side,

Subtract x^2 from both sides

Simplify left side and multiply out the square term of x+6

Subtract the left side of equation on both sides by itself to get zero on the left side. That is

Simplifying both sides of equation yields

Step 3. This is now a quadratic equation where we can use the quadratic formula.

where a=2, b=-12, c=-36

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=432 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8.19615242270663, -2.19615242270663. Here's your graph:

Step 4. Pick the positive number since we have only positive lengths. In this case, it's 8.196. so
Length of one leg

Length of other Leg

Length of hypotenuse.

You can use the Pythagorean Theorem to check if its close to verify your answer.

For Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.

For more info, contact Professor John Santiago at john@e-liteworks.com
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