Question

1. a square has an area of 100 cm². it is dilated by a scale factor of 4. jenny thinks the area of the new square will be 800 cm². veronica thinks the area of the new square will be 1,600 cm². who is correct and why? explain with at least one complete sentence.

Explanation:

Step1: Recall the formula for the area of a square after dilation

When a square (or any two - dimensional figure) is dilated by a scale factor \(k\), the area of the new figure \(A_{new}\) is related to the area of the original figure \(A_{old}\) by the formula \(A_{new}=k^{2}A_{old}\).

Step2: Identify the values of \(k\) and \(A_{old}\)

We are given that \(k = 4\) (scale factor) and \(A_{old}=100\space cm^{2}\) (area of the original square).

Step3: Calculate the area of the new square

Substitute the values into the formula \(A_{new}=k^{2}A_{old}\).

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Answer:

Veronica is correct. When a square (a two - dimensional figure) is dilated by a scale factor \(k\), the area of the new square is \(k^{2}\) times the area of the original square. Here, \(k = 4\) and \(A_{old}=100\space cm^{2}\). Using the formula \(A_{new}=k^{2}A_{old}\), we get \(A_{new}=4^{2}\times100=1600\space cm^{2}\).