FINDING SCALE FACTOR OF SIMILAR FIGURES AND FIND PERIMETER

The figures in each pair are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas.

Problem 1 :

Solution :

Ratio of corresponding sides = 2 : 4

Ratio of perimeter = a : b

= 2 : 4

a : b = 1 : 2

Ratio of area = a² : b²

= 1² : 2²

a² : b² = 1 : 4

Problem 2 :

Solution :

Ratio of corresponding sides = 15 : 25

Ratio of perimeter = a : b

= 15 : 25

a : b = 3 : 5

Ratio of area = a² : b²

= 3² : 5²

a² : b² = 9 : 25

Problem 3 :

Solution :

Ratio of corresponding sides = 8 : 6

Ratio of perimeter = a : b

= 8 : 6

a : b = 4 : 3

Ratio of area = a² : b²

= 4² : 3²

a² : b² = 16 : 9

Find the scale factor and the ratio of perimeters for each pair of similar figures.

Problem 4 :

Two regular octagons with areas 4 ft² and 16 ft²

Solution :

a² : b² = 4 : 16

a : b = √4 : √16

a : b = 2 : 4

a : b = 1 : 2

Problem 5 :

Two trapezoids with areas 49 cm² and 9 cm²

Solution :

a² : b² = 49 : 9

a : b = √49 : √9

a : b = 7 : 3

Problem 6 :

Two equilateral triangles with areas 16√3 ft² and √3 ft²

Solution :

a²: b² = 16√3: √3

a: b = 4: 1

Problem 7 :

Two circles with areas 2π cm² and 200π cm²

Solution :

a² : b² = 2π : 200π

a : b = 1 : 100