Answer:
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[tex]_{T}[/tex] = 64 feet
∵ At the same time, a girl 5 feet tall standing near the tree
∴ H[tex]_{G}[/tex] = 5 feet
∵ She casts a shadow that is 8 feet long
∴ L[tex]_{G}[/tex] = 8 feet
The ratios between the shadows and the heights of the tree and the girl are proportional
∵ [tex]\frac{H_{T}}{H_{G}}[/tex] = [tex]\frac{L_{T}}{L_{G}}[/tex]
→ Substitute their values in the equivalent ratios
∴ [tex]\frac{H_{T}}{5}[/tex] = [tex]\frac{64}{8}[/tex]
→ By using cross multiplication
∴ H[tex]_{T}[/tex] × 8 = 5 × 64
∴ 8H[tex]_{T}[/tex] = 320
→ Divide both sides by 8
∴ H[tex]_{T}[/tex] = 40 feet
∴ 40 feet represents the height of the tree
