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

40 feet represents the height of the tree ⇒ H

Step-by-step explanation:

Let us solve the question using the proportional

∵ A tree casts a shadow 64 feet long

∴ L = 64 feet

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

∴ H = 5 feet

∵ She casts a shadow that is 8 feet long

∴ L = 8 feet

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

∵ =

→ Substitute their values in the equivalent ratios

∴ =  

→ By using cross multiplication

∴ H × 8 = 5 × 64

∴ 8H = 320

→ Divide both sides by 8

∴ H = 40 feet

∴ 40 feet represents the height of the tree

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step-by-step explanation: