SOLUTION: The width of a rectangular TV screen is 5.7 in. more than the height. If the diagonal is 27.0 in., find the dimensions of the screen.

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Question 956293: The width of a rectangular TV screen is 5.7 in. more than the height. If the diagonal is 27.0 in., find the dimensions of the screen.
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
Let the height be x.
Then the width is (x+5.7).
The diagonal is 27.0 in.
x^2+(x+5.7)^2=27^2
x^2+x^2+11.4x+32.49=729
2x^2+11.4x-696.51=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B11.4x%2B-696.51+=+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=%2811.4%29%5E2-4%2A2%2A-696.51=5702.04.

Discriminant d=5702.04 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11.4%2B-sqrt%28+5702.04+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2811.4%29%2Bsqrt%28+5702.04+%29%29%2F2%5C2+=+16.0279633435389
x%5B2%5D+=+%28-%2811.4%29-sqrt%28+5702.04+%29%29%2F2%5C2+=+-21.7279633435389

Quadratic expression 2x%5E2%2B11.4x%2B-696.51 can be factored:
2x%5E2%2B11.4x%2B-696.51+=+2%28x-16.0279633435389%29%2A%28x--21.7279633435389%29
Again, the answer is: 16.0279633435389, -21.7279633435389. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B11.4%2Ax%2B-696.51+%29

Height=16.027
Width=21.727