SOLUTION: I'm having a hard time figuring this out. A 50-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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm having a hard time figuring this out. A 50-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      Log On


   

Question 366856: I'm having a hard time figuring this out. A 50-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 10 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.I appreciate all the help I can get.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A 50-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 10 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.I appreciate all the help I can get.
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Draw the picture.
Draw a horizontal line segment (the bridge).
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Draw a vertical support under the middle of the line segment (the brace)
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Draw a line segment connecting the base of the support to one
end of the bridge, thus forming a right triangle.
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hypotenuse = 50
leg = span = x+10 ft.
leg = support = x ft.
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Solve for "x":
x^2 + (x+10)^2 = 50^2
2x^2 + 20x + 100 = 2500
x^2 + 10x - 1200 = 0
(x-30)(x+40) = 0
Positive solution:
x = 30 ft (length of the support
x+10 = 40 ft (length of the span)
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Cheers,
Stan H.