Question 548519
A 20-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 4 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.
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Draw the picture:
You have a right triangle with:
hypotenuse = 20 ft
height = x
base = x+4
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Equation:
x^2 + (x+4)^2 = 20^2
x^2 + x^2 + 8x + 8 = 400
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2x^2 + 8x - 392 = 0
x^2 + 4x - 196 = 0
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I graphed the quadratic and found x = 12.14 ft (height)
base = x+4 = 16.14 ft.
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You could use the quadratic formula.
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Cheers,
Stan H.
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