Question

rectangle r with side lengths 4 and 6 is dilated by a scale factor of 2. what are the side lengths of the resulting rectangle? a. 2 and 3 b. 10 and 15 c. 8 and 12 d. 6 and 9

Explanation:

Step1: Recall dilation formula

When a rectangle is dilated by a scale - factor \(k\), the new side lengths are given by \(l_{new}=k\times l_{old}\), where \(l_{old}\) are the original side lengths and \(k\) is the scale - factor.

Step2: Calculate new side lengths

The original side lengths of the rectangle are \(l_1 = 4\) and \(l_2=6\). The scale - factor \(k = 2\).
For the first side: \(l_{1new}=2\times4 = 8\).
For the second side: \(l_{2new}=2\times6 = 12\).

Answer:

C. 8 and 12