Question

A person who is 70 inches tall cast a shadow that is 54 inches long. If a tree casts a shadow that is 28 feet long at the same time, then how hall is the tree to the nearest foot?
1) 22 feet
2) 30 feet
3) 36 feet
4) 42 feet

Answer 1

$\text{A person who is 70 inches tall cast a shadow that is 54 inches long. }\\ \text{We need to find the length of the tree that casts a shadow that }\\ \text{is 28 feet long at the same time}.\\ \text{for that we use the ratio. Let the length of the tree be x feet.}\\ \\ \text{so using ratio, we have}\\ \\ \frac{70}{54}=\frac{x}{28}\\ \\ \text{on cross multiplying, we get}$

$70\times 28=54\times x\\ \\ \Rightarrow 1960=54x\\ \\ \text{now divide both sides by 54, we get}\\ \\ \frac{1960}{54}=\frac{54x}{54}\\ \\ \Rightarrow 36.29=x$

Hence the height of the tree to the nearest foot is: 36 feet

Hence option (3) is correct.

Answer 2

The answer is 36 feet, so number 3