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In a parallelogram $ABCD$ , if $AB = 5cm, BC = 4cm$ ,then $A C^{2} + B D^{2} =$

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$40 c m$

$82 c m$

$41 c m$

$81 c m$

answer is B.

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Detailed Solution

We know that $A C^{2} + B D^{2} = A B^{2} + B C^{2} + C D^{2} + A D^{2}$

$A C^{2} + B D^{2} = 5^{2} + 4^{2} + 5^{2} + 4^{2}$

$= 2 (25 + 16)$

$= 2 \times 41$

$= 82 c m$

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