Question

A rectangle is reduced by a scale factor of One-fourth.

A large rectangle has a length of 16 and width of 12. A smaller rectangle has length of 4 and width of 3.

Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options.
StartFraction 4 over 16 EndFraction
(StartFraction 4 over 16 EndFraction) squared
StartFraction 12 over 192 EndFraction
StartFraction 4 squared over 12 squared EndFraction
(StartFraction 3 over 12 EndFraction squared

Answer 1

(StartFraction 4 over 16 EndFraction) squared

StartFraction 12 over 192 EndFraction

(StartFraction 3 over 12 EndFraction squared

Explanation:

Ratio of areas = (ratio of sides)²

Answer 2

(4/16)^2

(3/12)^2

12/192

Explanation:

We can write the ratio by taking the smaller length over the larger length

4 / 16

1/4

To find the area ratio

We take the scale factor and square it

I remember length is in units, area is in units ^2 so the area ratio is in scale factor squared

(1/4)^2

1/16

We can also look at the scale factor squared before we simplified it

(4/16) ^2

We also could look at the width ratio

3/12 and square it

(3/12)^2

Looking for the third choice

12/192 simplifies to 1/16