Question

If the perimeter of a rectangular plot is 68meters and the length of its diagonal is 26 meters , find its area.

Answer 1

here is your answer...
the perimeter of the rectangular plot is 68 meters.
the length of its diagonal is 26 meters..
so imagine the length of the plot is a meters and breadth is b meters.
so, According to the question...


$2(a + b) = 68 \\ or \: (a + b) = 34 \:$
hence the diagonal is 26 meters
$\sqrt{ {a}^{2} + {b}^{2} } = 26 \\ or \: \: {a}^{2} + {b}^{2} = 676 \\ or \: \: {(a + b)}^{2} - 2ab = 676 \\ or \: \: {34}^{2} - 2ab = 676 \\ or \: \: 2ab \: = 1156 - 676 \\ or \: \: 2ab = 480 \\ or \: \: ab = 240 \: {cm}^{2} \: \: (answer)$
so the area of the rectangular plot is 240 cm^2
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