The tree in the illustration casts a shadow $c = 6$ feet long, while a person $a = 6$ feet tall casts a shadow $b = 4$ feet long.
Find the height of the tree.
A) $\frac { 3 } { 12 }$
B) 15
C) $\frac { 1 } { 9 }$
D) 9
E) none of these

Question

The tree in the illustration casts a shadow $c = 6$  feet long, while a person $a = 6$  feet tall casts a shadow $b = 4$  feet long. 
Find the height of the tree. 
A) $\frac { 3 } { 12 }$ 
B) 15 
C) $\frac { 1 } { 9 }$ 
D) 9 
E) none of these

Quizplus · Accepted Answer

We can use proportions to solve the problem. Let x be the height of the tree.

Then, we have:

$$\frac {a}{b} = \frac {x}{c}$$
$$\frac {6}{4} = \frac {x}{6}$$
$$\frac {3}{2} = \frac {x}{6}$$
$$x = \frac {3}{2} \times 6$$
$$x=9$$

Therefore, the height of the tree is 9 feet. The answer is choice D.

The Tree in the Illustration Casts a Shadow c=6c = 6c=6

The Tree in the Illustration Casts a Shadow $c = 6$