Question

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

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length.
In \(\triangle NOP\), if \(Q\), \(R\), \(S\) are mid - points. Then \(QR=\frac{1}{2}NP\), \(RS = \frac{1}{2}NO\), \(SQ=\frac{1}{2}OP\)
Given \(NP = 6\), \(NO=8\), \(OP = 6\)

Step2: Calculate the lengths of the sides of \(\triangle QRS\)

\(QR=\frac{1}{2}\times6 = 3\)
\(RS=\frac{1}{2}\times8 = 4\)
\(SQ=\frac{1}{2}\times6=3\)

Step3: Calculate the perimeter of \(\triangle QRS\)

Perimeter \(P=QR + RS+SQ\)
\(P=3 + 4+3\)

Answer:

\(10\)