Question

The length of a rectangle is thrice its breadth and the length of its diagonal is $8\sqrt{10}\mathrm{cm}.$. The perimeter of the rectangle is
(a) $15\sqrt{10}\mathrm{cm}$
(b) $16\sqrt{10}\mathrm{cm}$
(c) $24\sqrt{10}\mathrm{cm}$
(d) 64 cm

Answer 1

(d) 64 cm

Let the breadth of the rectangle be x cm.
∴ Length of the rectangle = 3x cm
We know:
$$\begin{gathered} \mathrm{Diagonal}=\sqrt{(\mathrm{Length}{)}^2+(\mathrm{Breadth}{)}^2} \\ \Rightarrow 8\sqrt{10}=\sqrt{x^2+(3x{)}^2} \\ \Rightarrow 8\sqrt{10}=\sqrt{x^2+9x^2} \\ \Rightarrow 8\sqrt{10}=x\sqrt{10} \\ \Rightarrow x=8 \end{gathered}$$

Now,
Breadth of the rectangle = x = 8 cm
Length of the rectangle = 3x = 24 cm
Perimeter of the rectangle$=2(\mathrm{Length}+\mathrm{Breadth})=2(8+24)=64\mathrm{cm}$