Question

The sides of a triangle are $5cm,6cm$ and $7cm$. One more $\Delta$ is formed by joining the midpoints of the sides. The perimeter of the second $\Delta$ is:

• A. $18cm$
• B. $12cm$
• C. $9cm$
• D. $6cm$

Answer 1

The correct option is C $9cm$

Perimeter of $△ABC$ = $AB+BC+AC=5+6+7=18cm$

Since, points $P,Q,R$ are the mid-points of $△ABC$

$AP=BP=\frac{1}{2}AB=\frac{1}{2}\times 5=2.5cm$

Similarly, $AQ=QC=\frac{1}{2}AC=\frac{1}{2}\times 6=3cm$

∴ Perimeter of $△PQR=\frac{1}{2}\times Perimeterof△ABC$

∴ Perimeter of $△PQR=\frac{1}{2}\times 18=9cm$.