CTET 2 Math and Science 21 Jan 2024 Paper

Longer parallel side $=25\mathit{c}\mathit{m}$
Shorter parallel side $=11\mathit{c}\mathit{m}$
Distance between parallel sides (height) $=12\mathit{c}\mathit{m}$
Area $=1∕2\times$ (sum of parallel sides) $\times$ height
Area $=1∕2\times \left(25+11\right)\times 12$
Area of the trapezium $=216\mathit{c}{\mathit{m}}^2$
Now, the area of the rectangle should be equal to this.
The sides of the rectangle are in the ratio $3:2$, so if we take the longer side as 3 x , the shorter side will be 2 x .
Area of the rectangle $=$ length $\times$ breadth
$216=3\mathit{x}\times 2\mathit{x}$
$216=6{\mathit{x}}^2$
${\mathit{x}}^2=36$
$\mathit{x}=6$
Therefore, the longer side of the rectangle $=3\mathit{x}=18\mathit{c}\mathit{m}$, and the shorter side $=2\mathit{x}=12\mathit{c}\mathit{m}$.
Perimeter $=2\times ($ length + breadth $)$
Perimeter $=2\times \left(18+12\right)$
Perimeter $=60\mathit{c}\mathit{m}$