Kyra wants to make the area of her rectangular closet 9 times larger than the size it currently is. What scale factor should she use to dilate the dimensions of the closet?

Answer 1

Since you find the area by multiplying the length times the width, each should 3 times it's length.

Let's say the closet is currently 3 ft x 5 ftThat makea it 15 sq ft, right? How do we make it 135 sq ft?

3(3) x 5(3) = 9 x 15 = 135

Your scale factor is 3.

Answer 2

Hi Jazmin - good question!

Let's start with the formula for area of a rectangle:

Area = Length x Width = L x W

If I want the area to increase by a factor of 9, I have to do the same to both sides of the equation.

9 x Area = 9(L x W)

Now here is the trick. The question asks what "scale factor" you should use, meaning that you have to multiply both the length and the width of the closet by the same number to increase the area.

Let the scale factor equal s

9 x Area = 9(L x W) = sL x sW

Therefore,

9 x Area = 9(L x W) = s²(L x W)

s² = 9

s = 3

Since I'm trying to increase the area by a factor of 9, if I increase the length by a factor of 3, and the width by a factor of 3, they resulting area will increase by 3 x 3 which equals 9.