SOLUTION: The width of a rectangular gate is 2 meters(m) larger than it's height. The diagonal brace measures sqrt 6m. Find the width and height.

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Question 99597: The width of a rectangular gate is 2 meters(m) larger than it's height. The diagonal brace measures sqrt 6m. Find the width and height.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a^2+b^2=c^2
h^2+(h+2)^2=6
h^2+h^2+4h+4=6
2h^2+4h-2=0
h=.414214... m height(quadratic formula below)
h+2=2.414214... m width
check:
.414214...^2+2.414214...^2=6
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-2+=+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=%284%29%5E2-4%2A2%2A-2=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+32+%29%29%2F2%5C2+=+0.414213562373095
x%5B2%5D+=+%28-%284%29-sqrt%28+32+%29%29%2F2%5C2+=+-2.41421356237309

Quadratic expression 2x%5E2%2B4x%2B-2 can be factored:
2x%5E2%2B4x%2B-2+=+%28x-0.414213562373095%29%2A%28x--2.41421356237309%29
Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-2+%29