Question 155

In a rhombus ABCD, $$\angle$$A = 60° and AB. = 12 cm. Then the diagonal BD is

Solution

Given : $$\angle$$A = 60° and AB = 12 cm

To find : BD = ?

Solution : Since, all the sides of a rhombus are equal, => AB = AD

=> $$\angle$$ABD = $$\angle$$ADB

Now, in $$\triangle$$ABD

=> $$\angle$$ABD + $$\angle$$ADB + $$\angle$$A = 180°

=> 2$$\angle$$ABD = 120°

=> $$\angle$$ABD = $$\angle$$ADB = $$\angle$$A = 60°

=> ABD is equilateral triangle.

=> AB = AD = BD = 12 cm

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