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?

The scale factor is equal to

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

we have

substitute and solve for z

------> scale factor

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm