# SOLUTION: Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures&#8730;6m. Find the width and height.

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: Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures√6m. Find the width and height.
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In a rectangle, the one side is always longer than the other.
We mark "x"= height.
And the other side is 2m longer than this, so "x+2m"=the longer side (accdg. to your problem is the width).
Since we have a brace of , go by Pyth. Theorem to solve the other sides.

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 Solved by pluggable solver: SOLVE quadratic equation with variable 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=8 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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Thank you,
Jojo