Question

preimage image scale factor = 1/4 ? 5 cm a = 20 cm² given the area, what is the length of the missing side in the preimage? 8 cm 16 cm 4 cm 20 cm

Explanation:

Step1: Find the width of the image

The area of the image rectangle is \( A = 20 \, \text{cm}^2 \) and length is \( 5 \, \text{cm} \). Using the area formula \( A = \text{length} \times \text{width} \), we solve for width:
\( \text{width} = \frac{A}{\text{length}} = \frac{20}{5} = 4 \, \text{cm} \).

Step2: Apply the scale factor to find the preimage width

The scale factor from preimage to image is \( \frac{1}{4} \), meaning the image dimensions are \( \frac{1}{4} \) of the preimage. Let the preimage width be \( x \). Then:
\( \frac{1}{4}x = 4 \). Solving for \( x \):
\( x = 4 \times 4 = 16 \, \text{cm} \).

Answer:

16 cm