Question

In a rhombus abcd angle a=60 ,side ab=6cm then find out diagonal bd=?

Answer 1

In

In ΔABC∠A=60ΔABC∠A=60

AB=6cmAB=6cm

In rhombus all sides are equal .

=> AB=AD=6cmAB=AD=6cm

=> ∠B=∠D=6cm∠B=∠D=6cm

[Since equal sides subtend equal angle ]

Hence BD=6cmBD=6cm as it is equilateral triangle .

Answer : 6

Answer 2

In a rhombus ABCD ,

∠A= 60° ( Given in question )

Length of AB = 6 cm

Length of diagonal BD = ? (We have to find this)

NOTE:- Rhombus has four sides and every four sides of rhombus are equal . For example : rhombus PQRS has PQ= 8cm=QR= 8cm=RS = 8cm= PS = 8cm .

Here, In a rhombus ABCD ,

AB=6cm = BC = CD= AD=6cm ( rhomhus has all sides equal )

∠A= 60° = ∠C= 60° ( opposite angles of rhombus are equal)

So, in rhombus ABCD , BD and AC are diagonals .

So If we consider BC as diagonal,

Then BC divides the rhombus ABCD in two equilateral triangles.

Therefore,

∆ABD & ∆ BCD are two equilateral triangles from Rhombus ABCD.

In ∆ABD,

AB=6cm (given)

AD= 6cm ( AB=AD=6cm ,as rhombus has four equal sides )

∠A= 60°

So , BD= 6cm (AB=BD=6cm because All sides of equilateral triangle are equal)

Hence , BD = 6cm.