Question

2. Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10.

Rectangle C has length 30 and width 15.
a. Is Rectangle A a scaled copy of Rectangle B? If so, what is the scale factor?
b. Is Rectangle B a scaled copy of Rectangle A? If so, what is the scale factor?
C. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.
d. Is Rectangle A a scaled copy of Rectangle C? If so, what is the scale factor?

Answer 1

Rectangle B is a scaled copy of rectangle A.

Enlargement scale factor = 1.25

Explanation:

Rectangle A:

Length = 12 units

Width = 8 units

Rectangle B:

Length = 15 units

Width = 10 units

Rectangle C:

Length = 30 units

Width = 15 units

Rectangle B length ÷ rectangle A length = rectangle B width ÷ rectangle A width = 1.25

i.e
`(15)/(12)` =
`(10)/(8)` = 1.25

Hence rectangle B is a scaled copy of rectangle A and the scale factor of enlargement is 1.25

Answer 2

a) Yes. Rectangle A is a scaled copy of rectangle B.

b) Yes. Rectangle B is a scaled copy of rectangle A.

d) No. Rectangle A is not a scaled copy of rectangle C.

Explanation:

Rectangle A has dimensions 12x8 and

rectangle B has length 15x10

We see that sides of A and B are proportional because

`(12)/(15) =(8)/(10)`

So we say that since sides are proportional A and B are similar or scaled copy of each other.

Since A is smaller and B is bigger,

A is 0.8 scaled copy of B.

Similarly B has

Enlargement scale factor = 1.25

Rectangle C has 30x15

i.e. not proportion with sides of A and B.

Hence we find that C is neither a scaled copy of A nor B.