SOLUTION: Can someone help please? # 80. 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 hei

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Question 156090This question is from textbook elementary and intermediate algebra
: Can someone help please? # 80. 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.
Thank you This question is from textbook elementary and intermediate algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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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Draw the picture
Let the height be "x" meters
Then the width is "x+2" meters
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Draw the diagonal = sqrt(6) meters
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EQUATION:
Use Pythagoras to solve for "x":
x^2 + (x+2)^2 = [sqrt(6)]^2
2x^2 + 4x + 4 = 6
2x^2 + 4x -2 = 0
x^2 + 2x -1 = 0
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Use the Quadratic Formula:
x = [-2 +- sqrt(4 -4*1*-1)]/2
x = [-2 +- sqrt(8)]/2
Positive solution:
x = [-2 + 2sqrt(2)]/2
x = [-1 + sqrt(2)]
x = 0.414 meters (height of the rectangle)
x+2 = 2.414 meters (width of the rectangle)
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Cheers,
Stan H.