Let ABCD be the given rectangle.
BC = 16cm
Area of rectangle = length × breadth
Area of ABCD = BC × AB
∴ 192 = I6 × AB
∴ AB = \(\frac{192}{16}\)
= 12 cm
Now, in ∆ABC, ∠B = 90° [Angle of a rectangle]
∴ AC2 = AB2 + BC2 [Pythagoras theorem]
= 122 + 162
= 144 + 256
= 400
∴ AC = \(\sqrt{400}\) [Taking square root of both sides]
= 20cm
∴ The diagonal of the rectangle is 20 cm.