What is the perimeter of the parallelogram JKLM, whose co-ordinates are J(-5 , 2), K ( -2 , 6), L(5, 6), M (2, 2) ?

30 units

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24 units

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28 units

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21 units

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Solution

The correct option is A 24 units
Perimeter of the parallelogram $J K L M = 2 (J K + K L)$
Distance between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ can be calculated using the formula $\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$
$H e n c e, l e n g t h o f$ JK = $\sqrt{{(- 2 + 5)}^{2} + {(6 - 2)}^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5 u n i t s$
$A n d l e n g t h o f K L$ = $\sqrt{{(5 + 2)}^{2} + {(6 - 6)}^{2}} = \sqrt{49 + 0} = 7 u n i t s$
Hence, Perimeter of the parallelogram $J K L M = 2 (J K + K L) = 2 (5 + 7) = 24 u n i t s$

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