Madhya Pradesh Police Exam Model Paper 2

Given:
Area of rectangular carpet = $120{\mathit{m}}^2$
Perimeter of rectangular carpet = 46 m
Formula used:
Perimeter of the rectangle $=2\left(\mathit{l}+\mathit{b}\right)$
Area of the rectangle = lb
Diagonal of the rectangle $=\sqrt{\left({\mathit{l}}^2+{\mathit{b}}^2\right)}$
Calculation:
According to the question
2(l + b) = 46
⇒ (l + b) = 23
Also, lb = 120
As we know,
${\left(\mathit{l}+\mathit{b}\right)}^2={\mathit{l}}^2+{\mathit{b}}^2+2\mathit{l}\mathit{b}$
$\Rightarrow 232={\mathit{l}}^2+{\mathit{b}}^2+2\times 120$
$\Rightarrow {\mathit{l}}^2+{\mathit{b}}^2=529\mathit{–}240$
$\Rightarrow {\mathit{l}}^2+{\mathit{b}}^2=289$
∴ Diagonal $=\sqrt{\left({\mathit{l}}^2+{\mathit{b}}^2\right)}=\sqrt{289}=17\mathit{m}$