SOLUTION: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures rr 6 meters. find the width and height.
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Question 287984: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures rr 6 meters. 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 than its height. The diagonal brace measures rr 6 meters. find the width and height.
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Let height be x meters
Then width is "x+2" meters.
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Use Pythagoras to find width and height:
Equation:
x^2 + (x+2)^2 = 6^2
x^2 + x^2 + 4x + 4 = 36
2x^2 + 4x - 32 = 0
x^2 + 2x - 16 = 0
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x = [-2 +- sqrt(4 - 4*-16)]/2
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x = [-2 +- sqrt(68)]/2
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x = [-2 +- 2sqrt(17)]/2
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x = [-1 +-sqrt(17)]
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Positive solution:
x = -1+sqrt(17) is appoximately 3.1231m (width)
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x+2 = 5.1231m (length)
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Cheers,
Stan H.
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