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

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Question 174606: Diagonal brace. The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures squared 6m . Find the width and height.


Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Let h = height
then
h+2 = width
.
Applying Pythagorean theorem we have:
h^2 + (h+2)^2 = 6^2
h^2 + (h^2+4h+4) = 36
2h^2 + 4h + 4 = 36
2h^2 + 4h - 32 = 0
h^2 + 2h - 16 = 0
.
Applying the quadratic formula yields:
x = {3.123, -5.123}
.
Tossing out the negative solution we have:
height = 3.123 meters
width = h+2 = 5.123 meters
.
Details of quadratic follows:
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=68 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.12310562561766, -5.12310562561766. Here's your graph:
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