SOLUTION: 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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Question 78137: 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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Let h=height, w=width
So we have

Since the diagonal is the hypotenuse, we can say

Substitute 2+h into w

foil the parenthesis

Combine like terms and reduce to 6

Subtract 6 from both sides

Combine like terms
Now use the quadratic formula to find the value of L:
 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=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:

Ignoring the negative answer we get:

So use this to find w

So the height is 0.414 m and the width is 2.414 m approximately