The length of a rectangle is thrice its breadth and the length of its diagonal is

(d) 64 cm

Let the breadth of the rectangle be x cm.
∴ Length of the rectangle = 3x cm
We know:

Diagonal $=\sqrt{(\text { Length })^{2}+(\text { Breadth })^{2}}$

$\Rightarrow 8 \sqrt{10}=\sqrt{x^{2}+(3 x)^{2}}$

$\Rightarrow 8 \sqrt{10}=\sqrt{x^{2}+9 x^{2}}$

$\Rightarrow 8 \sqrt{10}=x \sqrt{10}$

$\Rightarrow x=8$

Now,
Breadth of the rectangle = x = 8 cm
Length of the rectangle = 3x = 24 cm

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