Question 138

If length of each side of a rhombus ABCD is 16 cm and ∠ABC = 120$$^\circ$$, then what is the length (in cm) of BD?

Solution

Given : BC = 16 cm and $$\angle$$ ABC = $$120^\circ$$

Diagonals of a rhombus bisect each others at right angle.

Thus, $$\angle$$ OBC = $$\frac{1}{2}\times120^\circ=60^\circ$$

In $$\triangle$$ OBC,

=> $$cos(\angle OBC)=\frac{OB}{BC}$$

=> $$cos(60^\circ)=\frac{OB}{16}$$

=> $$\frac{1}{2}=\frac{OB}{16}$$

=> $$OB=\frac{16}{2}=8$$ cm

$$\therefore$$ BD = $$2\times8=16$$ cm

=> Ans - (C)

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