Question

The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. The area of the rectangle is

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

Answer 1

(c) 192 cm²

Let ABCD be the rectangular plot.
Then, AB = 16 cm
AC = 20 cm

Let BC = x cm
From right triangle ABC:
AC² = AB² + BC²
⇒ (20)² = (16)² + x²
⇒ x² = (20)² - (16)² ⇒ {400 - 256} = 144
⇒ x = $\sqrt{144}$ = 12
∴ BC = 12 cm
∴ Area of the plot = (16 × 12) cm² = 192 cm²