Question

An acute angle made by a side of parallelogram with other pair of parallel sides is 60°. if the distance between these parallel sides is 6√3, the other side is:

Answer 1

The other side is 12.

Answer 2

$Given \: ABCD \: is \: a \: parallelogram .\\AB \parallel DC \: and\: AD\parallel BC . \\\angle {DAB} = 60\degree , \\distance \: between \: two \: parallel \:sides \: AB \:and \:DC (h) = 6\sqrt{3}\:cm$

$In \: \triangle ADM, \angle {AMD} = 90\degree$

$Sin 60\degree = \frac{MD}{AD}$

$\implies \frac{\sqrt{3}}{2} = \frac{6\sqrt{3}}{AD}$

$\implies AD = 6\sqrt{3}\times \frac{2}{\sqrt{3}}$

$\implies AD = 6 \times 2 = 12 \:cm$

Therefore.,

$\red{ Required \: length \:of \:the \:side }\green {= 12 \:cm }$

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