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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?

Respuesta :

MrRoyal

Answer:

1. Yes

2. Yes

3. No

Step-by-step explanation:

Given

Rectangle A:

[tex]Length = 12; Width = 8[/tex]

Rectangle B:

[tex]Length = 15; Width = 10[/tex]

Rectangle C:

[tex]Length = 30; Width = 15[/tex]

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.

[tex]Ratio = \frac{A}{B}[/tex]

For Length:

[tex]Ratio = \frac{12}{15}[/tex]

[tex]Ratio = 0.8[/tex]

For Width:

[tex]Ratio = \frac{8}{10}[/tex]

[tex]Ratio = 0.8[/tex]

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.

[tex]Ratio = \frac{A}{C}[/tex]

For Length:

[tex]Ratio = \frac{12}{30}[/tex]

[tex]Ratio = 0.4[/tex]

For Width:

[tex]Ratio = \frac{8}{15}[/tex]

[tex]Ratio = 0.53[/tex]

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