Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

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(√3)  ∴ Ratio=(1/(√3))

$$\mathrm{shorter}\:\mathrm{diagonal}\:=\:\mathrm{a} \\ $$$$\mathrm{longer}\:\mathrm{diagonal}\:=\:\mathrm{a}\sqrt{\mathrm{3}} \\ $$$$\therefore\:\mathrm{Ratio}=\frac{\mathrm{1}}{\sqrt{\mathrm{3}}} \\ $$

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(√3).Thus,(d_(sh) /d_l )=(a/(a(√3)))=(1/(√3)).Hence,choose D is the  answer

$$\mathrm{Denote}\:\mathrm{by}\:\mathrm{a}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{parallelogram}.\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{shorter}\:\mathrm{diagonal}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{a} \\ $$$$\left(\mathrm{since}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{side}\:\mathrm{of}\:\:\mathrm{the}\:\mathrm{regular}\:\mathrm{triangle}.\mathrm{The}\:\mathrm{length}\right. \\ $$$$\mathrm{of}\:\mathrm{longer}\:\mathrm{diagonal}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{two}\:\mathrm{times}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of} \\ $$$$\mathrm{altitude}\:\mathrm{of}\:\mathrm{regular}\:\mathrm{triangle}\:\mathrm{i}.\mathrm{e}\:\mathrm{it}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\mathrm{a}\sqrt{\mathrm{3}}.\mathrm{Thus},\frac{\mathrm{d}_{\mathrm{sh}} }{\mathrm{d}_{\mathrm{l}} }=\frac{\mathrm{a}}{\mathrm{a}\sqrt{\mathrm{3}}}=\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}.\mathrm{Hence},\mathrm{choose}\:\mathrm{D}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\: \\ $$

Answered by bobhans last updated on 06/Jun/20

length of shorter diagonal x = (√(2s^2 −2s^2 ×cos 60^o )) = s  length of longer diagonal y =(√(2s^s −2s^2 ×cos 120^o ))= s(√3)  then ratio =(s/(s(√3))) = 1 : (√3)

$$\mathrm{length}\:\mathrm{of}\:\mathrm{shorter}\:\mathrm{diagonal}\:\mathrm{x}\:=\:\sqrt{\mathrm{2s}^{\mathrm{2}} −\mathrm{2s}^{\mathrm{2}} ×\mathrm{cos}\:\mathrm{60}^{\mathrm{o}} }\:=\:\mathrm{s} \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{longer}\:\mathrm{diagonal}\:\mathrm{y}\:=\sqrt{\mathrm{2s}^{\mathrm{s}} −\mathrm{2s}^{\mathrm{2}} ×\mathrm{cos}\:\mathrm{120}^{\mathrm{o}} }=\:\mathrm{s}\sqrt{\mathrm{3}} \\ $$$$\mathrm{then}\:\mathrm{ratio}\:=\frac{\mathrm{s}}{\mathrm{s}\sqrt{\mathrm{3}}}\:=\:\mathrm{1}\::\:\sqrt{\mathrm{3}}\: \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com