Question

Two large poles of heights 20 meters and 30 meters respectively each have a wire running from the top of one to the base of the other. The wires are pulled tight and cross at a particular point between the two poles. At what height above the ground in meters do the wires intersect?

Answer 1

The wires meet at 12 meters from ground.

Step-by-step explanation:

Let the distance of point of intersection from ground be x.

Lets assume a pole is placed at x height as middle pole.

The distance between base of 20 meters pole and middle pole is a.

The distance between base of 30 meters pole and middle pole is b.

Now, the similarity triangles are obtained.

x/20 = a/(a + b) → (equation 1)

And

x/30 = b/(a + b) → (equation 2)

On adding equation (1) and (2), we get,

x/20 + x/30 = a/(a + b) + b/(a + b)

x/20 + x/30 = (a + b)/(a + b)

x/20 + x/30 = 1

(3x + 2x)/60 = 1

5x/60 = 1

∴ x = 60/5 = 12 m