Question

Triangle EFG has side lengths of 5 feet, 12 feet, and 13 feet. Triangle KLM is similar to triangle EFG with a scale factor of 4. What are the side lengths of triangle KLM?

Answer 1

Answer: The answer is 20 feet, 48 feet and 52 feet.

Explanation: Given in the question and shown in the attached figure that ΔEFG has side lengths EF = 4 feet, FG = 12 feet and EG = 13 feet. ΔKLM is similar to ΔEFG and is produced after a dilation of scale factor 4.

We are to find the side lengths of ΔKLM.

Since ΔEFG and ΔKLM are similar to each other, so the ratio of their sides will be proportional. That is

`(KL)/(EF)=(LM)/(FG)=(MK)/(GE)=4.`

So, KL = 4 × EF = 4 × 5 = 20 feet,

LM = 4 × FG = 4 × 12 = 48 feet

and

MK = 4 × GE = 4 × 13 = 52 feet.

Thus, the side lengths of ΔKLM are 20 feet, 48 feet and 52 feet.