Question-96936

Question Number 96936 by joki last updated on 05/Jun/20

Commented by PRITHWISH SEN 2 last updated on 05/Jun/20

shorter diagonal = a

longer diagonal = a \sqrt{3}

∴ Ratio = \frac{1}{\sqrt{3}}

Answered by 1549442205 last updated on 05/Jun/20

Denote by a the length of the side of parallelogram . Then

the length of shorter diagonal is equal to a

(since it is a side of the regular triangle . The length

of longer diagonal equal to two times the length of

altitude of regular triangle i . e it is equal to

a \sqrt{3} . Thus, \frac{d_{sh}}{d_{l}} = \frac{a}{a \sqrt{3}} = \frac{1}{\sqrt{3}} . Hence, choose D is the

answer

Answered by bobhans last updated on 06/Jun/20

length of shorter diagonal x = \sqrt{{2 s}^{2} - {2 s}^{2} \times \cos 60^{o}} = s

length of longer diagonal y = \sqrt{{2 s}^{s} - {2 s}^{2} \times \cos 120^{o}} = s \sqrt{3}

then ratio = \frac{s}{s \sqrt{3}} = 1 : \sqrt{3}

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