Question

Fill in the blank with Yes or No. Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. 1. Is Rectangle A a scaled copy of Rectangle B? 2. Is Rectangle B a scaled copy of Rectangle A? 3. Is Rectangle A a scaled copy of Rectangle C?

Answer 1

1. Yes

2. Yes

3. No

Explanation:

Given

Rectangle A:

`Length = 12; Width = 8`

Rectangle B:

`Length = 15; Width = 10`

Rectangle C:

`Length = 30; Width = 15`

Solving (1): Is Rectangle A a scaled copy of Rectangle B?

To do this, we simply determine the ratio of the length and width of both rectangles;

i.e.

`Ratio = (A)/(B)`

For Length:

`Ratio = (12)/(15)`

`Ratio = 0.8`

For Width:

`Ratio = (8)/(10)`

`Ratio = 0.8`

Since both ratios are the same, then this statement is true

Solving (2): Is Rectangle B a scaled copy of Rectangle A?

This is the inverse of (1) calculated above.

Since (1) is true, then (2) is also true

3. Is Rectangle A a scaled copy of Rectangle C?

To do this, we simply determine the ratio of the length and width of both rectangles;

i.e.

`Ratio = (A)/(C)`

For Length:

`Ratio = (12)/(30)`

`Ratio = 0.4`

For Width:

`Ratio = (8)/(15)`

`Ratio = 0.53`

Since both ratios are the not same, then this statement is false