Question

The length of diagonals of parallelogram are $4$ cm and $6$ cm. Find out the perimeter of Parallelogram which is formed when the mid points of adjacent sides are joined.

• A. $5$ cm
• B. $10$ cm
• C. $15$ cm
• D. $20$ cm

Answer 1

The correct option is B $10$ cm

In $△ABC$
$P$ and $Q$ are mid points of sides $AB$ and $BC$ respectively so by mid point theorem we know $PQ=\frac{1}{2}AC$,
Similarly, in $△ADC$
$RS=\frac{1}{2}AC$

And similarly in $△BDC\&△BDA$,
$PS=RQ=\frac{1}{2}BD$
So,
$PQ+RS=\frac{1}{2}AC+\frac{1}{2}AC$
$PQ+RS=AC$
and $PS+RQ=BD$
So, $\text{perimeter}=PQ+RQ+RS+PS$
$\text{perimeter}=AC+BD$
$\text{perimeter}=6+4$
$\text{perimeter}=10$ cm

Hence, correct option is $\left(b\right)$.