SOLUTION: The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height.
Question 203369: The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The width of a rectangular gate is 2 meters (m) larger that its height. The diagnoal brace measures square root6m. Find the width and height.
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Draw a picture of a rectangle.
Label the width as (x+2) meters.
Label the height as (x) meters.
Lsbel the diagonal as sqrt(6) meters.
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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
Use the quadratic formula to solve for "x":
x = [-2 +- sqrt(4 -4*1*-1]/2
x = [-2 +- sqrt(8)]/2
x = [-1 +- sqrt(2)]
Positive solution:
x = sqrt(2) - 1 = 0.414 meters (this is the height of the rectangle)
x+2 = 2.414 meters (this is the width of the rectangle)
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Cheers,
Stan H.
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