Question

1. a triangle △jkl with side lengths 4, 6, and 8 is dilated by k = 3. what are the side lengths of the dilated triangle?

a. 4,6,8
b. 12,18,24
c. 6,9,12
d. 12,15,24

Explanation:

Step1: Recall dilation formula

When a figure is dilated by a scale - factor \(k\), the new side - length \(s_{new}\) is given by \(s_{new}=k\times s_{old}\), where \(s_{old}\) is the original side - length.

Step2: Calculate new side - lengths

Given \(k = 3\) and original side - lengths \(s_1=4\), \(s_2 = 6\), \(s_3=8\).
For the first side: \(s_{new1}=k\times s_1=3\times4 = 12\).
For the second side: \(s_{new2}=k\times s_2=3\times6 = 18\).
For the third side: \(s_{new3}=k\times s_3=3\times8 = 24\).

Answer:

b. 12, 18, 24