Discussion
Find perimeter of △LMN, if midpoints of its sides are joined to form △PQR. Also midpoints of △PQR are joined to get △CDE and CD=3, DE=8 and CE=4.
Answer: C
The triangle formed by joining the midpoints of a triangle's sides is the medial triangle. Each of its sides is half the parallel side of the original, by the midpoint theorem, so its perimeter is exactly half.
\[ P_{\triangle CDE} = 3 + 8 + 4 = 15 \]
\( \triangle CDE \) is the medial triangle of \( \triangle PQR \):
\[ P_{\triangle PQR} = 2 \times 15 = 30 \]
and \( \triangle PQR \) is the medial triangle of \( \triangle LMN \):
\[ P_{\triangle LMN} = 2 \times 30 = 60 \]
Each step outward doubles the perimeter, so two steps multiply it by four.
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