Let ABCD be a rectangle and AB and BC are the adjacent sides of length 30cm and 16cm respectively.
Let AC be the diagonal.
In ∆CBA, using Pythagoras Theorm,
(Perpendicular)2 + (Base)2 = (Hypotenuse)2
⇒ (AB)2 + (BC)2 = (AC)2
⇒ (30)2 + (16)2 = (AC)2
⇒ (AC)2 = 900 + 256
⇒ (AC)2 = 1156
⇒ AB = ±34
⇒ AB = 34 [taking positive square root]
Hence, the length of a diagonal of a rectangle is 34 cm
