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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=32 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:
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