ABCD का समचतुर्भुज है, जिसकी भुजा AB=4 cm तथा `angleABC=120^(@)` है।, तब विकर्ण BD की लम्बाई ज्ञात करे?

Options

A. 1 cm
B. 2 cm
C. 3 cm
D. 4 cm

Answer

D

Explanation

According to question, ltbr.
Given, `angleB=120^(@)`
In a rhombus diagonal are angle bisector and diagonal cut at right angle.
`therefore sin360^(@)=P/H=(BO)/(AB)`
`1/2 xx (BO)/4`
BO=2cm
`therefore BD=2 xx BO`
=`2 xx 2=4cm`
Alternate:-
`angleABC=1/2angleABC`
`=1/2xx120^(@) = 60^(@)`
`angleA=angleABD=angleADB=60i^(@)`
`therefore angleA=angleABD=angleADB=60^(@)`
`therefore DeltaABD=`Equilateral triangle
So AB=BD=4cm