Question

if a triangle with sides 3 cm, 4 cm, and 5 cm is dilated by a scale factor of 2, what are the new side lengths?
a. 12 cm, 16 cm, 20 cm
b. 6 cm, 8 cm, 10 cm
c. 9 cm, 12 cm, 15 cm
d. 6 cm, 7 cm, 8 cm

Explanation:

Step1: Recall dilation formula

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

Step2: Calculate new side lengths

For the side of length \(3\) cm: \(l_1 = 2\times3=6\) cm.
For the side of length \(4\) cm: \(l_2 = 2\times4 = 8\) cm.
For the side of length \(5\) cm: \(l_3 = 2\times5=10\) cm.

Answer:

B. 6 cm, 8 cm, 10 cm