Find height of intersection of 6-foot, 12-foot poles

[sarnak282]

I need to find the height at which two lines intersect.

There is a 6 foot pole and a 12 foot pole. A line is stretched from the top of the 12 foot pole to the base of the 6 foot pole. A second line is stretched from the top of the 6 foot pole to the base of the 12 foot pole. Find the height at which the lines cross. I have no idea where to start. I know that I can prove the two triangles created similar. I have no idea if this helps me any.

You are also given that the distance from the base of the 6 foot pole to a perpendicular line drawn down from the point of intersection is x and y is the length from the perpendicular line to the 12 foot pole. You are also given that this length does not affect the answer. As, I can reason that no matter how far apart the poles are placed, the point of intersection between the two lines would remain constant.

Thanks for your help.

 

[tkhunny]

Think real hard on those similar triangles.

Lable the height of the intersection, m.

Similarity suggests:

\(\displaystyle \L\;\frac{12}{x+y}\;=\;\frac{m}{x}\)

\(\displaystyle \L\;\frac{6}{x+y}\;=\;\frac{m}{y}\)

That's about all you need. There is a little algebra remaining.