# SOLUTION: I have been stuck on this question for a while because I do not understand how I would answer it or even put it into a polynomial. The question is: A 5-ft diagonal brace on a

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: I have been stuck on this question for a while because I do not understand how I would answer it or even put it into a polynomial. The question is: A 5-ft diagonal brace on a       Log On

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 Question 592695: I have been stuck on this question for a while because I do not understand how I would answer it or even put it into a polynomial. The question is: A 5-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 1 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace. Answer by htmentor(789)   (Show Source): You can put this solution on YOUR website!A 5-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 1 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace. ========================= Let h = the height reached by the support Then the horizontal distance = h + 1 This forms a right triangle with hypotenuse = 5: Using the Pythagorean theorem we can write h^2 + (h+1)^2 = 5^2 Solve for h: h^2 + h^2 + 2h + 1 = 25 2h^2 + 2h - 24 = 0 This can be factored as 2(h+4)(h-3) = 0 Taking the positive solution, we have h=3 So the vertical distance is 3, and the horizontal distance is 4. Note that this is a 3-4-5 right triangle