Question

Find the length of a diagonal of a rectangle whose adjacent sides are 30 cm and 16 cm.

Answer 1

Let ABCD be the rectangle with diagonals AC and BD meeting at O.
According to the question:
AB = CD = 30 cm and BC = AD = 16 cm

Applying Pythagoras theorem in right-angled triangle ABC, we get:

$$\begin{gathered} A{C}^2=A{B}^2+B{C}^2={30}^2+{16}^2=900+256=1156 \\ AC=\sqrt{1156}=34\mathrm{cm} \end{gathered}$$

Diagonals of a rectangle are equal.
Therefore, AC = BD = 34 cm