Question

a rhombus has sides of length 10 cm and one angle measures 60 degree what will be the length of the shorter diagonal​

Answer 1

ABCD is a rhombus .

AB = BC = CD = DA = 10 cm ( given )

AC and BD are two diagonals .

AC and BD perpendicularly bisect each other.

$\angle {DAB} + \angle {ABC} = 180\degree$

$\pink { Adjacent \: angles \:are \: supplementary }$

$\implies \angle {ABC} = 180 - 60 = 120\degree$

$\triangle ABD} \: is \: an \: equilateral \: triangle$

Therefore.,

$AB = BD = DA = 10\:cm$

$\red { Shortest \: diagonal \:(BD) }\green {= 10\:cm }$

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