Fun Math Problem 'Cussed Ladders'

[Gamo]

According to Csaba the answer is wrong and the answer is 4.8 feet. Ha ha ha just kidding Csaba your answer is right. Your equation is very clever way to do it.

According to the article in the magazine said Maybe the simplest way is to lable the distance on the ground from each building to line X as a and b, which allows you to set up two simple ratios based on similar triangles:

12/(a+b)=x/a and 8/(a+b)=x/b

Multiplying both equations through and substituting for the common term yields
what may have been intuitively obvious: b=3/2 a. Now you can rewrite the above equations using 3/2 a in place of b and 5/2 a in place of a+b. Solving both equations for X (the a's cancel) gives the height above the ground at which the ladders intersect: 4.8 feet.


Now you are ready to try the second variation of the cussed ladders. This time, ladder lengths are given as 40 and 30 feet, and they cross at a point 10 feet from the ground. How far apart are the buildings against which the ladders are leaning?
Because in this puzzle you have three dimensions given instead of two, it may at first glance look to be the easier problem. It is not. This one will require that you use your calculator--as well as your head.


Gamo