Question

A string of length $12$ units is bent first into square $PQRS$ and then into a right angled $△PQT$ by keeping the side $PQ$ of the square fixed and other is one more than its side. The area of $PQRS$ equals

• A. $ar\left(△PQT\right)$
• B. $\frac{3}{2}ar\left(△PQT\right)$
• C. $2.ar\left(△PQT\right)$
• D. None of these

Answer 1

Answer: (B)

$\frac{3}{2}ar\left(△PQT\right)$

Side of square $=3$ unit

$\Rightarrow ar\left(PQRS\right)={\left(3\right)}^2=9$ sq. unit

One side of $△PQT$ is the side $PQ$ of the square i.e., $3$ units

The other is one more than its side i.e., $(3+1)=4$ units

$\Rightarrow ar\left(△PQT\right)=\frac{1}{2}\left(3\right)\left(4\right)=6$ sq. units

$\Rightarrow ar\left(PQRS\right)=\frac{3}{2}\left\{ar\left(△PQT\right)\right\}$