Scale Factor Quiz

What is the scale factor of two similar figures if the length of one side in the first figure is 4 cm and the corresponding side in the second figure is 8 cm?

• 2

• 0.5

• 3

• 10

Answer explanation

The scale factor of two similar figures is obtained by dividing the length of a side in the second figure by the corresponding side length in the first figure. Here, the length of the side in the second figure is 8 cm and in the first figure is 4 cm. So, the scale factor is 8/4 = 2, which is the correct answer.

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.2

If the scale factor between two similar figures is 3, and the length of one side in the first figure is 5 cm, what is the length of the corresponding side in the second figure?

• 8

• 15

• 10

• 12

Answer explanation

In the question, it is given that the scale factor between two similar figures is 3. This means that each dimension of the second figure is 3 times larger than the corresponding dimension in the first figure. Therefore, if one side in the first figure is 5 cm, the length of the corresponding side in the second figure would be 3 times 5 cm, which equals 15 cm. Thus, the correct answer is 15 cm.

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.2

In a similar figure, if the scale factor is 2 and the area of the first figure is 36 square units, what is the area of the second figure?

• 144

• 9

• 72

• 18

Answer explanation

In similar figures, the ratio of the areas is the scale factor squared. Here, the scale factor is 2, so the ratio of the areas is 2^2 = 4. Thus, to find the area of the second figure, we multiply the area of the first figure (36 square units) by 4, which gives us 144 square units.

Tags

CCSS.7.G.A.1

CCSS.7.G.B.6

If the scale factor between two similar figures is 0.5, and the length of one side in the first figure is 10 cm, what is the length of the corresponding side in the second figure?

• 2 cm

• 7 cm

• 15 cm

• 5 cm

Answer explanation

The question states that the scale factor between two similar figures is 0.5. Scale factor is the ratio of the lengths of corresponding sides of two similar geometric figures. Therefore, to find the length of the corresponding side in the second figure, we multiply the length of the side in the first figure by the scale factor i.e., 10 cm * 0.5 = 5 cm. So, the correct answer is 5 cm.

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.2

CCSS.7.RP.A.3

In a similar figure, if the scale factor is 0.75 and the perimeter of the first figure is 24 cm, what is the perimeter of the second figure?

• 18 cm

• 20 cm

• 16 cm

• 22 cm

Answer explanation

The question asks for the perimeter of a similar figure with a scale factor of 0.75 from a figure with a perimeter of 24cm. Since the scale factor is 0.75, the perimeter of the similar figure will be 0.75 times the original. So, 0.75 * 24cm equals 18 cm. Therefore, the correct answer is 18 cm.

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.2

If the scale factor between two similar figures is 4, and the area of the first figure is 64 square units, what is the area of the second figure?

• 32

• 1024

• 256

• 16

Answer explanation

The scale factor is the ratio of the lengths of two corresponding sides of two similar figures. If the scale factor is 4, and the area of the first figure is 64, the area of the second figure will be 64 multiplied by the scale factor squared, because area is a two-dimension property. So, the area of the second figure is 64*4*4 which equals 256 square units.

Tags

CCSS.7.G.A.1

CCSS.7.G.B.6

In a similar figure, if the scale factor is 1.5 and the length of one side in the first figure is 8 cm, what is the length of the corresponding side in the second figure?

• 12 cm

• 10 cm

• 14 cm

• 16 cm

Answer explanation

In similar figures, corresponding sides are proportionate. The scale factor tells us how much larger or smaller one figure is compared to the other. Here, the scale factor is 1.5, meaning the second figure is 1.5 times larger than the first. So, to find the length of the corresponding side in the second figure, multiply the length of the side in the first figure (8 cm) by the scale factor (1.5). This gives us 12 cm, which is the correct answer.

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.2

If the scale factor between two similar figures is 0.2, and the length of one side in the first figure is 15 cm, what is the length of the corresponding side in the second figure?

• 0.3

• 3

• 0.5

• 1.5

Answer explanation

The scale factor between two similar figures is a ratio that relates corresponding side lengths. If the scale factor is 0.2 and one side in the first figure is 15 cm, we multiply 0.2 by 15 to find the length of the corresponding side in the second figure, which gives us 3 cm.

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.2

In a similar figure, if the scale factor is 0.6 and the perimeter of the first figure is 30 cm, what is the perimeter of the second figure?

• 15 cm

• 12 cm

• 18 cm

• 24 cm

Answer explanation

The perimeter of the second figure is obtained by multiplying the perimeter of the first figure by the scale factor. So, 30 cm times 0.6 equals 18 cm. Thus, the correct answer is 18 cm.

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.2

If the scale factor between two similar figures is 2.5, and the area of the first figure is 100 square units, what is the area of the second figure?

• 250

• 400

• 900

• 625

Answer explanation

In case of similar figures, the ratio of their areas is the square of the scale factor. Here, the scale factor is 2.5. So, the area of the second figure will be (2.5)^2 times the area of the first figure. That is, 2.5^2 * 100 = 625 square units.

Tags

CCSS.7.G.A.1

CCSS.7.G.B.6

CCSS.7.RP.A.2