Q17 of 33 Page 108

In the rhombus ABCD, the length of the side AB is 4 cm. and ∠BCD = 60°. Let us write the length of the diagonal BD.


Let us make a diagram from given information as above,


As, ABCD is a rhombus and all sides of a rhombus are equal


AB = BC = CD = DA = 4 cm


Now, In ΔBCD


BC = CD [sides of rhombus are equal]


∠CBD = ∠CDB [Angles opposite to equal sides are equal]


In ΔBCD


∠CBD + ∠CDB + ∠BCD = 180°


⇒ ∠CBD + ∠CBD + 60° = 180°


⇒ 2∠CBD = 120°


⇒ ∠CBD = 60°


So, we have ∠CBD = ∠CDB = ∠BCD = 60°


As, all angles are 60°, ΔBCD is an equilateral triangle


∴ BC = CD = BD [All sides of an equilateral triangle are equal]


⇒ BD = 4 cm


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