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.

Explanation:

Step1: Recall mid - point theorem

The segment connecting 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 the sides of $\triangle OPQ$ are $PQ = 4$, $OQ=3$, $OP = 3$. Then the corresponding sides of $\triangle LMN$ are: Let the side of $\triangle LMN$ corresponding to $PQ$ be $LN$, to $OQ$ be $LM$, and to $OP$ be $MN$. So $LN = 2\times4=8$, $LM=2\times3 = 6$, $MN=2\times3=6$.

Step3: Calculate perimeter of $\triangle LMN$

Perimeter of $\triangle LMN=LN + LM+MN=8 + 6+6=20$.

Answer:

20