Question

Find the length of diagonal of the rectangle whose sides are 16 cm and 12 cm.

Answer 1

Suppose the sides are x and y of lengths 16 cm and 12 cm, respectively.

Let the diagonal be z cm.

Clearly, the diagonal is the hypotenuse of the right triangle with legs x and y.

By Pythagoras theorem:
$$\begin{gathered} z^2=x^2+y^2 \\ \Rightarrow z^2={16}^2+{12}^2 \\ \Rightarrow z^2=256+144 \\ \Rightarrow z^2=400 \\ \Rightarrow z^2={20}^2 \\ \Rightarrow z=20 \end{gathered}$$

Hence, the length of the diagonal is 20 cm.