Two similar triangles have a scale factor of 2 : 3. For numbers 7a – 7d, determine whether each statement about the triangles is true or false. 7a. The ratio of their perimeters is 2 : 3. True or False
7b. The ratio of their areas is 4 : 6. True or False
7c. Their perimeters could be 14 cm and 21 cm. True or False
7d. Two corresponding sides could be 6 in and 7 in. True or False

Step-by-step explanation:

Two similar triangles have a scale factor of 2 : 3.

7a. The ratio of their perimeters is 2 : 3.

As the sides are 2 : 3, the perimeters which are sums of all sides will also be 2 : 3

True

7b. The ratio of their areas is 4 : 6. True or False

As the sides are 2 : 3, the areas which are the products of two sides will be in the ratio of 2*2 : 3*3 = 4 : 9

False

7c. Their perimeters could be 14 cm and 21 cm. True or False

As the perimeter ratio for 14cm and 21 cm is 14 : 21 = 2 : 3 which complies with 7a. So they could be the perimeters.

True

7d. Two corresponding sides could be 6 in and 7 in. True or False

As the corresponding sides of 6in and 7in, the ratio is 6 : 7 and is different from 2 : 3.  So they cannot be corresponding sides.

False

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step-by-step explanation: