We have been given that side length OQ of our prei-mage is 9.4 units and side length OQ' after dilation is 17.1 units. Since our pre-image (original image) is smaller than our new image, so our scale factor (r) will be greater than 1.

Since we know that in a dilation, the sides of the pre-image and the corresponding sides of the image are proportional, so we will use proportion to find a scale factor our given side lengths as:

$\frac{OQ'}{OQ}=\frac{17.1}{9.4}$

$\frac{OQ'}{OQ}=1.8191$

Upon multiplying both sides of our equation by OQ we will get,

$\frac{OQ'}{OQ}\times OQ=1.8191\times OQ$

$OQ'=1.8191\times OQ$

Upon rounding our answer to nearest hundredths place we will get,

$OQ'\approx 1.82\times OQ$

Since side length OQ' is 1.82 times side length OQ, therefore, our scale factor (r) will be 1.82 units.

8 0

3 years ago

The length of each side of the square is decreased by 2 inches, so the perimeter is now 48 inches . What was the original length

Jet001 [13]

X=original length of each side of the square.
perimeter: sum of all sides=4(length of the side)
The length of each side of the new square will be= (x-2)
we can suggest this equation:

4(x-2)=48

We solve this equation:
4(x-2)=48
4x-8=48
4x=48+8
4x=56
x=56/4
x=14

Answer: the original length of each side of the square would be 14 in.

5 0

4 years ago