SOLUTION: A triangle has base 12 centimeters and 8 centimeters . How much much do you have to increase each dimension equally so that the area is tripled?

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Question 550046: A triangle has base 12 centimeters and 8 centimeters . How much much do you have to increase each dimension equally so that the area is tripled?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle has base 12 centimeters and 8 centimeters . How much much do you have to increase each dimension equally so that the area is tripled?
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Area = b*h/2 = 48 sq cm
48*3 = 144
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(12 + x)*(8 + x)/2 = 144
x%5E2+%2B+20x+%2B+96+=+288
x%5E2+%2B+20x+%2B+-+192+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B20x%2B-192+=+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=%2820%29%5E2-4%2A1%2A-192=1168.

Discriminant d=1168 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+1168+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+1168+%29%29%2F2%5C1+=+7.08800749063506
x%5B2%5D+=+%28-%2820%29-sqrt%28+1168+%29%29%2F2%5C1+=+-27.0880074906351

Quadratic expression 1x%5E2%2B20x%2B-192 can be factored:
1x%5E2%2B20x%2B-192+=+%28x-7.08800749063506%29%2A%28x--27.0880074906351%29
Again, the answer is: 7.08800749063506, -27.0880074906351. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B20%2Ax%2B-192+%29

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Add ~ 7.088 to b and to h