A 10-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 2 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.

Question

anonymous · Answer

Not enough info...?

anonymous · Answer

thats all i have

anonymous · Answer

we have been working on factoring if that helps

anonymous · Answer

polynomials

anonymous · Answer

Well, I have an image of your bridge. The brace extends 2 feet past where it passes the bridge... but we don't know where it starts. We would need to know either how far from the side of the bridge it's start point is, or at least it's trajectory...

anonymous · Answer

it is probably to late but this is what I got... Let X denote the vertical distance that it spans. Then, since it spans 1 more foot horizontally, it spans x+2 feet horizontally. 
x^2+(x+2)^2=10^2
=>x^2+(x^2+4x+4)=100 by expanding
=>2x^2+4x+4=100
=>2x^2+4x-96=0, by setting the right side equal to zero.
=>2(x+8)(x-6)=0, by factoring
=>x=-8 and x=6 by the zero-product property
Since length cannot be negative, x=6.
Therefore, the brace spans 6 ft vertically and 6+2=8 ft horizontally
I got some help with this problem, so I believe it is correct... Hope this helps! good luck