Question

If the length of a diagonal of a rectangle of length 16 cm is 20 cm, then its area is

(a) 192 cm² (b) 320 cm² (c) 160 cm² (d) 156 cm²

Answer 1

Here, l = 16 cm, Length of diagonal = 20 cm. Let b be the breadth of the rectangle.
In the right-angled triangle formed with the adjacent sides and the diagonal, using Pythagoras theorem, we get
$$\begin{gathered} l^2+b^2={\left(\mathrm{Diagonal}\right)}^2 \\ \Rightarrow {16}^2+b^2={20}^2 \\ \Rightarrow b^2={20}^2-{16}^2=144 \\ \Rightarrow b=12\mathrm{cm} \end{gathered}$$
Area of rectangle = l $\text{×}$ b = 16 $\text{×}$ 12 = 192 cm²
Hence, the correct option is (a).