Question

The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.

Answer 1

Let a and b be the sides of the rectangle
Since the perimeter is 92 m, we have,
2( a + b ) = 92
⇒ a + b = 46 m                      ...(1)
Also, given that diagonal of a trapezium is 34 m.
⇒ a² + b² = 34²                     ....(2)

We know that
( a + b )² - a² - b² = 2ab

From equations (1) and (2), we have,
46² - 34² = 2ab
⇒ 2ab = 960
⇒ ab = ${\displaystyle \frac{960}{2}}$
⇒ ab = 480m².