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

Answer:

The scale factor is equal to $3$

Step-by-step 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

$z^{2}=\frac{x}{y}$

we have

$x=900\ ft^{2}$

$y=100\ ft^{2}$

substitute and solve for z

$z^{2}=\frac{900}{100}$

$z^{2}=9$

$z=3$ ------> scale factor