Question

A tree cast a shadow 64 feet long. At the same time, a girl 5 feet tall

standing near the tree cast a shadow that is 8 feet long. Which of the
following represents the height of the tree?
F. 61 feet
G. 51 feet
H. 40 feet
J. 25 feet

Answer 1

40 feet represents the height of the tree ⇒ H

Explanation:

Let us solve the question using the proportional

∵ A tree casts a shadow 64 feet long

∴ L
`_(T)` = 64 feet

∵ At the same time, a girl 5 feet tall standing near the tree

∴ H
`_(G)` = 5 feet

∵ She casts a shadow that is 8 feet long

∴ L
`_(G)` = 8 feet

The ratios between the shadows and the heights of the tree and the girl are proportional

∵
`(H_(T))/(H_(G))` =
`(L_(T))/(L_(G))`

→ Substitute their values in the equivalent ratios

∴
`(H_(T))/(5)` =
`(64)/(8)`

→ By using cross multiplication

∴ H
`_(T)` × 8 = 5 × 64

∴ 8H
`_(T)` = 320

→ Divide both sides by 8

∴ H
`_(T)` = 40 feet

∴ 40 feet represents the height of the tree