Question

similar figure word problems
name________
date______ period__
answer each question and round your answer to the nearest whole number.

1. a 6 ft tall tent standing next to a cardboard box casts a 9 ft shadow. if the cardboard box casts a shadow that is 6 ft long then how tall is it?
2. a telephone booth that is 8 ft tall casts a shadow that is 4 ft long. find the height of a lawn ornament that casts a 2 ft shadow.
3. a map has a scale of 3 cm : 18 km. if riverside and smithville are 54 km apart then they are how far apart on the map?
4. find the distance between riverside and milton if they are 12 cm apart on a map with a scale of 4 cm : 21 km.
5. a model house is 12 cm wide. if it was built with a scale of 3 cm : 4 m then how wide is the real house?
6. oak grove and salem are 87 mi from each other. how far apart would the cities be on a map that has a scale of 5 in : 29 mi?
7. a map has a scale of 2 in : 6 mi. if clayton and centerville are 10 in apart on the map then how far apart are the real cities?
8. a statue that is 12 ft tall casts a shadow that is 15 ft long. find the length of the shadow that a 8 ft cardboard box casts.

answer each question and round your answer to the nearest tenth.

1. a model house has a scale of 1 in : 2 ft. if the real house is 26 ft wide then how wide is the model house?
2. a 6.5 ft tall car standing next to an adult elephant casts a 33.2 ft shadow. if the adult elephant casts a shadow that is 51.5 ft long then how tall is it?
3. if a 42.9 ft tall flagpole casts a 253.1 ft long shadow then how long is the shadow that a 6.2 ft tall woman casts?
4. georgetown and franklin are 9.7 in apart on a map that has a scale of 1.1 in : 15 mi. how far apart are the real cities?

Explanation:

Step1: Set up proportion for problem 1

$\frac{6}{9} = \frac{x}{6}$

Step2: Solve for $x$ (problem1)

$9x = 6 \times 6 \implies x = \frac{36}{9} = 4$

Step3: Set up proportion for problem 2

$\frac{8}{4} = \frac{x}{2}$

Step4: Solve for $x$ (problem2)

$4x = 8 \times 2 \implies x = \frac{16}{4} = 4$

Step5: Set up proportion for problem3

$\frac{3}{18} = \frac{x}{54}$

Step6: Solve for $x$ (problem3)

$18x = 3 \times 54 \implies x = \frac{162}{18} = 9$

Step7: Set up proportion for problem4

$\frac{4}{21} = \frac{12}{x}$

Step8: Solve for $x$ (problem4)

$4x = 21 \times 12 \implies x = \frac{252}{4} = 63$

Step9: Set up proportion for problem5

$\frac{3}{4} = \frac{12}{x}$

Step10: Solve for $x$ (problem5)

$3x = 4 \times 12 \implies x = \frac{48}{3} = 16$

Step11: Set up proportion for problem6

$\frac{5}{29} = \frac{x}{87}$

Step12: Solve for $x$ (problem6)

$29x = 5 \times 87 \implies x = \frac{435}{29} = 15$

Step13: Set up proportion for problem7

$\frac{2}{6} = \frac{10}{x}$

Step14: Solve for $x$ (problem7)

$2x = 6 \times 10 \implies x = \frac{60}{2} = 30$

Step15: Set up proportion for problem8

$\frac{12}{15} = \frac{8}{x}$

Step16: Solve for $x$ (problem8)

$12x = 15 \times 8 \implies x = \frac{120}{12} = 10$

Step17: Set up proportion for problem9

$\frac{1}{2} = \frac{x}{26}$

Step18: Solve for $x$ (problem9)

$2x = 1 \times 26 \implies x = \frac{26}{2} = 13.0$

Step19: Set up proportion for problem10

$\frac{6.5}{33.2} = \frac{x}{51.5}$

Step20: Solve for $x$ (problem10)

$33.2x = 6.5 \times 51.5 \implies x = \frac{334.75}{33.2} \approx 10.1$

Step21: Set up proportion for problem11

$\frac{42.9}{253.1} = \frac{6.2}{x}$

Step22: Solve for $x$ (problem11)

$42.9x = 6.2 \times 253.1 \implies x = \frac{1569.22}{42.9} \approx 36.6$

Step23: Set up proportion for problem12

$\frac{1.1}{15} = \frac{9.7}{x}$

Step24: Solve for $x$ (problem12)

$1.1x = 15 \times 9.7 \implies x = \frac{145.5}{1.1} \approx 132.3$

Answer:

1. 4 ft
2. 4 ft
3. 9 cm
4. 63 km
5. 16 m
6. 15 in
7. 30 mi
8. 10 ft
9. 13.0 in
10. 10.1 ft
11. 36.6 ft
12. 132.3 mi