SOLUTION: Write the equation and then solve. a) One leg of a right triangle is four less than twice the other. The hypotenuse is 10. Find the length of each leg. Please help me solv

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Write the equation and then solve. a) One leg of a right triangle is four less than twice the other. The hypotenuse is 10. Find the length of each leg. Please help me solv      Log On

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Question 305289: Write the equation and then solve.
a) One leg of a right triangle is four less than twice the other.
The hypotenuse is 10. Find the length of each leg.

Please help me solve this equation.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation and then solve.
a) One leg of a right triangle is four less than twice the other.
The hypotenuse is 10. Find the length of each leg.
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1st side = x
2nd side = 2x-4
x%5E2+%2B+%282x-4%29%5E2+=+10%5E2
5x%5E2+-+16x+%2B+16+=+100
5x%5E2+-+16x+-+84+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-16x%2B-84+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-16%29%5E2-4%2A5%2A-84=1936.

Discriminant d=1936 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+1936+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+1936+%29%29%2F2%5C5+=+6
x%5B2%5D+=+%28-%28-16%29-sqrt%28+1936+%29%29%2F2%5C5+=+-2.8

Quadratic expression 5x%5E2%2B-16x%2B-84 can be factored:
5x%5E2%2B-16x%2B-84+=+%28x-6%29%2A%28x--2.8%29
Again, the answer is: 6, -2.8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-16%2Ax%2B-84+%29

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Ignore the negative solution
x = 6
2x - 4 = 8
--> 6, 8 & 10 triangle