A parallelogram and a rectangle having same base length and same height .If $P_{1}$ & $P_{2}$ be the perimeter of the parallelogram and the rectangle respectively, then which of the following is correct?

$P_{1} < P_{2}$

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$P_{1} = P_{2}$

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$P_{1} > P_{2}$

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$C a n^{'} t s a y$

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Solution

The correct option is C
$P_{1} > P_{2}$

Since parallelogram and rectangle having the same base length and height, both have same area.

Parallelogram ABDF and Rectangle ABCE have perimeter P1& P2 respectively.
Perimeter of rectangle = 2 (l + b)
Perimeter of parallelogram = 2(l0+b)
Since, l is the perpendicular distance between two line, it is the shortest distance between lines a and b
While, l0 is not perpendicular distance between two lines, it must be greater than l
so, perimeter of the parallelogram>perimeter of the rectangle.

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