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Question
The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.
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Solution
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 = `960/2`
⇒ ab = 480m2.
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