Question

A square has a side length of 36 feet. this square is dilated by a scale factor of 2/3 to create a new square. what is the side length of the new square?

Answer 1

Dilation by 2/3 means scaling.  It would be 2/3 of 36 which is 24

Answer 2

the side length of the new square is, 24 feet

Explanation:

Scale factor(k) is defined as the ratio of the dilated image to the Pre-image.

⇒
`k = \frac{\text{Dilated image}}{\text{Pre-image}}`

As per the statement:

A square has a side length of 36 feet. this square is dilated by a scale factor of 2/3

⇒Side length of the Pre-image square = 36 feet and k = 2/3

By definition we have;

`(2)/(3) = \frac{\text{New side length of the dilated image of square}}{36}`

Multiply both sides by 36 we have;

`(2)/(3) \cdot 36=\text{New side length of the dilated image of square}`

Simplify:

`\text{New side length of the dilated image of square} = 24` feet

therefore, the side length of the new square is, 24 feet