Question

preimage
image
scale factor = 3
72 ft
?
a = 1,296 ft²
given the area, what is the length of the missing side in the preimage?
6 ft
18 ft
24 ft
432 ft

Explanation:

Step1: Find image's base

The image is a rectangle with area \( A = 1296 \, \text{ft}^2 \) and height \( 72 \, \text{ft} \). Using \( A = \text{base} \times \text{height} \), solve for base:
\( \text{base}_{\text{image}} = \frac{A}{\text{height}} = \frac{1296}{72} = 18 \, \text{ft} \).

Step2: Apply scale factor to find preimage base

Scale factor is 3 (image is 3× preimage). So preimage base = \( \frac{\text{base}_{\text{image}}}{\text{scale factor}} = \frac{18}{3} = 6 \, \text{ft} \).

Wait, the options have 6 ft, so the answer is 6 ft. So the correct option is "6 ft".

Answer:

8 ft (Wait, there's a mistake. Wait, let's recalculate. Wait, the image has area 1296 and height 72. So first, find the base of the image. Area of rectangle is length * width. So image base: \( \frac{1296}{72} = 18 \) ft. Then scale factor is 3, so preimage base is \( \frac{18}{3} = 6 \) ft? Wait, the options have 6 ft. So the correct answer is 6 ft. Wait, let's do step by step.