Question

The area of a rectangular carpet is 120 m² and its perimeter is 46 m. The length of its diagonal is
(a) 15 m
(b) 16 m
(c) 17 m
(d) 20 m

Answer 1

(c) 17 m
Let the length and the breadth of the rectangle be L m and B m, respectively.

Area of the rectangular carpet = ($L\times B$) m²
$\Rightarrow LB=120...\left(\mathrm{i}\right)$
Perimeter of the rectangular carpet = $2(L+B)$
$$\begin{gathered} \Rightarrow 2(L+B)=46 \\ \Rightarrow (L+B)=\frac{46}{2} \\ \Rightarrow (L+B)=23...\left(\mathrm{ii}\right) \end{gathered}$$

$$\begin{gathered} \mathrm{Diagonal}\mathrm{of}\mathrm{the}rectangle\; =\sqrt{L^2+B^2}\mathrm{m} \\ =\sqrt{(L+B{)}^2-2LB}\mathrm{m} \\ =\sqrt{(23{)}^2-240}\mathrm{m}(\mathrm{from}\mathrm{equatio}n\mathrm{s}(\mathrm{i})\mathrm{and}(\mathrm{ii}\left)\right) \\ =\sqrt{529-240}\mathrm{m} \\ =\sqrt{289}\mathrm{m} \\ =17\mathrm{m} \end{gathered}$$