Question

The area of a garden in the shape of an irregular quadrilateral is 100 square feet. The gardener purchases adjacent land, resulting in a new garden that is the image of the original garden under a dilation. If the area of the image is 900 square feet, by which scale factor is the original garden dilated?

Answer 1

The scale factor is equal to
`3`

Explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the image

y----> the area of the original garden

so

`z^(2)=(x)/(y)`

we have

`x=900\ ft^(2)`

`y=100\ ft^(2)`

substitute and solve for z

`z^(2)=(900)/(100)`

`z^(2)=9`

`z=3` ------> scale factor