Question

question
triangle opq is formed by connecting the mid - points of the side of triangle lmn. the lengths of the sides of triangle opq are shown. find the perimeter of triangle lmn. figures not necessarily drawn to scale.
answer attempt 1 out of 2
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Explanation:

Step1: Recall mid - point theorem

The segment joining the mid - points of two sides of a triangle is half the length of the third side of the triangle.

Step2: Find side lengths of $\triangle LMN$

If $OP = 3$, then the side of $\triangle LMN$ parallel to $OP$ has length $2\times3 = 6$. If $PQ=4$, then the side of $\triangle LMN$ parallel to $PQ$ has length $2\times4 = 8$. If $OQ = 3$, then the side of $\triangle LMN$ parallel to $OQ$ has length $2\times3=6$.

Step3: Calculate perimeter of $\triangle LMN$

Perimeter $P=6 + 8+6=20$.

Answer:

20