Question

solve each problem. show your work.

1. a 4-ft-tall girl casts a 3-ft shadow. at the same time a tree casts a 15-ft shadow. how tall is the tree?
2. the scale on a scale drawing is \\(\frac{1}{3}\\) in. = 1 ft. a room on the drawing is \\(2\frac{2}{3}\\) in. long. what is the actual length of the room?

Explanation:

(Problem 11):

Step1: Set up proportion

$\frac{\text{Girl's height}}{\text{Girl's shadow}} = \frac{\text{Tree's height}}{\text{Tree's shadow}}$
$\frac{4}{3} = \frac{h}{15}$

Step2: Solve for tree height $h$

$h = \frac{4 \times 15}{3}$
$h = 4 \times 5 = 20$

(Problem 12):

Step1: Set up proportion

$\frac{\text{Drawing length}}{\text{Actual length}} = \frac{\frac{1}{3}}{1}$
$\frac{2\frac{2}{3}}{L} = \frac{1}{3}$

Step2: Convert mixed number to fraction

$2\frac{2}{3} = \frac{8}{3}$

Step3: Solve for actual length $L$

$L = \frac{8}{3} \times 3 = 8$

Answer:

1. The tree is 20 ft tall.
2. The actual length of the room is 8 ft.