Briefly

The rope between the posts

The rope between the posts

A 100 meter long rope is nailed at both ends at the top of two posts.

The posts are nailed to the ground and have a height above the ground of 90m and 70m respectively and are perpendicular to the ground. In addition, we know that the lowest point of the rope is 30m from the ground.

What is the distance between the posts?

Solution

The posts are glued next to each other. We know that the rope is nailed at the top of the two posts and that it hangs up to 30m from the ground. This means that it is 70 - 30 = 40m away from the top of the smallest post and 90 - 30 = 60m away from the top of the highest post. 40m + 60m = 100m which is the total length of the rope so there can be no separation between the two posts.