Problema Solution
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 than the height that it reaches on the side of the bridge. What is the horizontal and vertical distances spanned by this brace.
Answer provided by our tutors
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)