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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

User Annet
by
3.3k points

1 Answer

5 votes

Answer:

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

User Kvorobiev
by
3.4k points