ft 10 ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on a bridge. The horizontal distance that spans is 2ft longer than the height that reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.

Question

ft 10 ft diagonal  brace on a bridge connects a support of the center of the bridge to a side support on a bridge.  The horizontal distance that spans is 2ft longer than the height that reaches on the side of the bridge.  Find the horizontal  and vertical distances spanned by this brace.

anonymous · Answer

solve 
$$x^2+(x+2)^2=10^2$$

anonymous · Answer

$$x^2+x^2+4x+=100$$
$$2x^2+4x=100$$
$$x^2+2x=50$$
$$(x+1)^2=51$$
$$x+1=\sqrt{51}$$
$$x=-1+\sqrt{51}$$

gw2011 · Answer

I get an answer of: vertical=6 ft and horizontal=8 ft.  Here is how I got the answers:

Let x=Vertical Distance
Let x+2=Horizontal Distance

a^2+b^2=c^2
(x^2)+(x+2)^2=(10)^2
x^2+x^2+4x+4=100
2x^2+4x+4=100
2x^2+4x-96=0
(2x+16)(x-6)=0
2x+16=0
2x=-16
x=-8  This is not a solution because you can't have a negative number

x-6=0
x=6  This is the vertical distance
x+2=6+2=8  This is the horizontal distance