Question

the square below is the image of a square that was dilated by a scale factor of 3/2. find the area of the preimage, the original square, before its dilation. figures are not necessarily drawn to scale. 30

Explanation:

Step1: Find the side - length of the pre - image

Let the side - length of the pre - image be \(x\).
The scale factor of dilation is \(k=\frac{3}{2}\), and the side - length of the image is \(y = 30\).
We know that \(y=k\times x\), so \(x=\frac{y}{k}\).
Substituting \(y = 30\) and \(k=\frac{3}{2}\), we get \(x=\frac{30}{\frac{3}{2}}=30\times\frac{2}{3}=20\).

Step2: Calculate the area of the pre - image

The area of a square \(A=x^{2}\).
Since \(x = 20\), then \(A=20^{2}=400\).

Answer:

The area of the pre - image is \(400\).