(B) For any parallelogram with adjacent sides $a$ and $b$ and diagonals $d_1$ and $d_2$,the parallelogram law states: $d_1^2 + d_2^2 = 2(a^2 + b^2)$.G

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(B) For any parallelogram with adjacent sides $a$ and $b$ and diagonals $d_1$ and $d_2$,the parallelogram law states: $d_1^2 + d_2^2 = 2(a^2 + b^2)$.Given $a = 12\, cm$,$b = 14\, cm$,and $d_1 = 16\, cm$.Substituting the values into the formula:$16^2 + d_2^2 = 2(12^2 + 14^2)$$256 + d_2^2 = 2(144 + 196)$$256 + d_2^2 = 2(340)$$256 + d_2^2 = 680$$d_2^2 = 680 - 256 = 424$$d_2 = \sqrt{424} \approx 20.59\, cm \approx 20.6\, cm$.

Competitive Quantitative Aptitude Mensuration Measurement of Area

Medium

In a parallelogram,the lengths of adjacent sides are $12\, cm$ and $14\, cm$,respectively. If the length of one diagonal is $16\, cm$,then find the length of the other diagonal (in $cm$).

A
$24.8$
B
$20.6$
C
$22.4$
D
None of these

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In a parallelogram,the lengths of adjacent sides are $12\, cm$ and $14\, cm$,respectively. If the length of one diagonal is $16\, cm$,then find the length of the other diagonal (in $cm$).

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