SOLVING PROPORTIONS WORD PROBLEMS INVOLVING SIMILAR FIGURES

Answer each question and round your answer to the nearest whole number.

Problem 1 :

If a 6 ft tall tent casts a 10 ft long shadow then how long is the shadow that a 9 ft tall adult elephant casts?

Solution :

Let x be a length of the shadow.

Height of the tent casts = 6 ft

Length of the shadow = 10 ft

Height of a adult elephant casts = 9 ft

6 : 10 = 9 : x

6/9 = 10/x

Using cross multiplication.

6x = 90

Divide each side by 6.

6x/6 = 90/6

x = 15

So, length of the shadow is 15 ft.

Problem 2 :

A model plane has a scale of 1 in : 6 yd. If the model plane is 3 in tall then how tall is the real plane?

Solution :

Let x be the height of the real plane.

A model plane has a scale = 1 in : 6 yd

Height of the model plane = 3 in

1 : 6 = 3 : x

1/3 = 6/x

Using cross multiplication.

x = 18

So, height of the real plan is18 yd.

Problem 3 :

A particular motorcycle is 9 ft long. A model of it was built with a scale of 1 in : 3 ft. how long is the model?

Solution :

Length of the motor cycle = 9 ft

Scale factor of model to original = 1 in : 3 ft

Let x be a length of the model.

1 : 3 = x : 9

1/3 = x/9

Using cross multiplication.

3x = 9

Divide each side by 3.

3x/3 = 9/3

x = 3

So, the length of the model is 3 in.

Problem 4 :

A particular satellite is 15 m wide. A model of it was built with a scale of 1 cm : 5 m. How wide is the model?

Solution :

Wide of a particular satellite = 15 m

Scale of model to original = 1 cm : 5 m

Let x be the model of the wide.

1 : 5 = x : 15

1/5 = x/15

Using cross multiplication.

15 = 5x

Divide each side by 5.

15/5 = 5/5x

3 = x

So, width of the model is 3 cm.

Problem 5 :

A model train is 7 in tall. If it was built with a scale of 1 in : 2 ft then how tall is the real train?

Solution :

Height of a model train = 7 in

Scale factor of model to original = 1 in : 2 ft

Let x be a height of a real train.

1 : 2 = 7 : x

1/2 = 7/x

Using cross multiplication.

14 = x

So, height of a real train is14 ft.

Problem 6 :

Find the distance between Riverside and Victoria if they are 9 cm apart on a map with a scale of 1 cm : 18 km.

Solution :

Riverside and Victoria apart on a map = 9 cm

Scale = 1 cm : 18 km

Let the distance between Riverside and Victoria be x.

1 : 18 = 9 : x

1/18 = 9/x

Using cross multiplication.

x = 18 × 9

x = 162

So, the distance between Riverside and Victoria is 162 km.

Problem 7 :

Milton and San Jose are 9 in apart on a map that has a scale of 1 in ; 13 mi. How far apart are the real cities? 

Solution :

Distance between Milton and San Jose on the map = 9 in

A Scale of a map = 1 in : 13 mi

Let x be the distance between two cities.

1 : 13 = 9 : x

1/13 = 9/x

Using cross multiplication.

x = 117

So, distance of a real cities is117 mi.

Problem 8 :

A 15 ft tall statue standing next to an adult elephant casts a 18 ft shadow. If the adult elephant is 10 ft tall then how long is its shadow?

Solution :

Height of the statue = 15 ft

length of shadow = 18 ft

height of elephant = 10 ft

length of its shadow = x

15 : 18 = 10 : x

15/18 = 10/x

Using cross multiplication.

15x = 180

Divide each side by 15.

x = 12

So, length of the shadow is 12 ft .

Problem 9 :

Find the distance between Fairview and Riverside if they are 4 in apart on a map with a scale of 1 in : 3 mi.

Solution :

Let the distance between Fairview and Riverside be x.

Distance of a map = 4 in

A scale of a map = 1 in : 3 mi

1 : 3 = 4 : x

1/3 = 4/x

x = 12

So, the distance between Fairview and Riverside is 12 mi.

Problem 10 :

A globe that is 3 ft tall casts a shadow that is 7 ft iong. Find the length of the shadow that a 6 ft woman casts.

Solution :

Let x be a length of the shadow

Height of a globe = 3 ft

Length of the shadow = 7 ft

Height of the women = 6 ft

3 : 7 = 6 : x

3/6 = 7/x

Using cross multiplication.

3x = 7 × 6

3x = 42

Divide each side by 3.

x = 14

So, the length of the shadow is 14 ft.

Problem 11 :

A 6 ft tall man standing next to a tree casts a 8 ft shadow. If the tree is 15 ft tall then how long is its shadow?

Solution :

Let x be a length of the shadow of tree.

Height of the man = 6 ft

length of shadow of man = 8 ft

Height of a tree = 15 ft

6 : 8 = 15 : x

6/8 = 15/x

Using cross multiplication.

6x = 15 × 8

6x = 120

Divide each side by 6.

x = 20

So, length of the shadow is 20 ft.

Problem 12 :

A 8 ft tall telephone booth standing next to an adult giraffe casts a 4 ft shadow. If the adult giraffe is 14 ft tall then how long is its shadow?

Solution :

Let x be a length of the shadow of giraffe.

Height of the telephone booth = 8 ft

Length of its shadow = 4 ft

Height of the adult giraffe = 14 ft

8 : 4 = 14 : x

8/4 = 14/x

Using cross multiplication.

8x = 14 ×4

8x = 56

Divide each side by 8.

 x = 7

So, length of the shadow is 7 ft.