Question

triangle pqr is formed by connecting the midpoints of the side of triangle mno. the lengths of the sides of triangle pqr are shown. find the perimeter of triangle mno. figures not necessarily drawn to scale.

Explanation:

Step1: Recall mid - point theorem

The line segment joining the mid - points of two sides of a triangle is parallel to the third side and half its length.

Step2: Find side lengths of $\triangle MNO$

If the side lengths of $\triangle PQR$ are $PQ = 5$, $QR=6$, and $RP = 9$. Then the corresponding side lengths of $\triangle MNO$ are twice the side lengths of $\triangle PQR$. So the side lengths of $\triangle MNO$ are $2\times5 = 10$, $2\times6=12$, and $2\times9 = 18$.

Step3: Calculate perimeter of $\triangle MNO$

The perimeter $P$ of a triangle is the sum of its side lengths. So $P=10 + 12+18$.
$P=40$.

Answer:

$40$