Question

A length of a rope is is stretched between the top edge of a building and a stake in the ground. The head of the steak is at ground level. The rope also touches a tree that is growing halfway between the stake and the building. If the tree is 38 feet tall, how tall is the building?1: 38ft2: 19ft3: 76ft4: 57ft

Answer 1

Height of building is 76 feets

Explanation:

The scenario is illustrated in the attached photo. The stretched rope is seen coming from the top of the building, passing through the top of the tree which is halfway the height of the building and touching the state which is on the ground.

The distance, x of the tree to the building on the ground is equal to the distance, x of the tree from the stake, hence,

Distance of the stake from the building is 2x

Height of the tree = 38 feets

Height of the building = y feets

The triangles formed are similar triangles. Therefore,

38/x = y/2x

Cross multiplying

2x × 38 = x × y

xy = 76x

y = 76x/x = 76 feets