Question

preimage
image
scale factor = 1/4
?
a = 96 yd²
12
given the area, what is the length of the missing side in the preimage?
12 yd
8 yd
96 yd
32 yd

Explanation:

Step1: Find the width of the image

The area of the image rectangle is \( A = 96\space yd^2 \) and the length is \( 12\space yd \). Using the formula for the area of a rectangle \( A = l\times w \), we can find the width \( w \) of the image.
\( w=\frac{A}{l}=\frac{96}{12} = 8\space yd \)

Step2: Find the width of the pre - image

The scale factor from the pre - image to the image is \( \frac{1}{4} \). Let the width of the pre - image be \( W \) and the width of the image be \( w \). We know that \( w=\frac{1}{4}W \), so \( W = 4w \).
Substituting \( w = 8\space yd \) into the formula, we get \( W=4\times8 = 32\space yd \)

Step3: Relate to the missing side (assuming the missing side is the width of the pre - image)

Since the figure is a rectangle and we found the width of the pre - image (the missing side) to be \( 32\space yd \)

Answer:

32 yd