SOLUTION: a painting is 20 cm wider than its high. its area is 240cm^2. find the width and height of the painting

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Question 1013240: a painting is 20 cm wider than its high. its area is 240cm^2. find the width and height of the painting
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a painting is 20 cm wider than its high. its area is 240cm^2. find the width and height of the painting
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L*W = 240
W = L+20
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L*(L+20) = 240
L^2 + 20L - 240 = 0
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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-240+=+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-240=1360.

Discriminant d=1360 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+1360+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+1360+%29%29%2F2%5C1+=+8.43908891458577
x%5B2%5D+=+%28-%2820%29-sqrt%28+1360+%29%29%2F2%5C1+=+-28.4390889145858

Quadratic expression 1x%5E2%2B20x%2B-240 can be factored:
1x%5E2%2B20x%2B-240+=+%28x-8.43908891458577%29%2A%28x--28.4390889145858%29
Again, the answer is: 8.43908891458577, -28.4390889145858. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B20%2Ax%2B-240+%29

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L =~ 8.439
W =~ 28.439