SOLUTION: a=x b=x+12 C=60 help would be sooooo appreciated

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Question 984505: a=x
b=x+12
C=60
help would be sooooo appreciated
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Right triangle with sides a and b and hypotenuse c
You know that a%5E2+%2B+b%5E2+=+c%5E2
So plug in the given values
x%5E2+%2B+%28x%2B12%29%5E2+=+60%5E2
x%5E2+%2B+x%5E2+%2B+24x+%2B+144+=+3600
2x%5E2+%2B+24x+-+3456+=+0
x%2A2+%2B+12x+-+1728+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B-1728+=+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=%2812%29%5E2-4%2A1%2A-1728=7056.

Discriminant d=7056 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+7056+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+7056+%29%29%2F2%5C1+=+36
x%5B2%5D+=+%28-%2812%29-sqrt%28+7056+%29%29%2F2%5C1+=+-48

Quadratic expression 1x%5E2%2B12x%2B-1728 can be factored:
1x%5E2%2B12x%2B-1728+=+1%28x-36%29%2A%28x--48%29
Again, the answer is: 36, -48. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B-1728+%29


That yields two solutions. But one is negative. A triangle can't have a side with negative length, so use the positive one. Once you know a, then b = 12 more
a=36
b=48