1.

two opposite angle of a rhombus are 120 each. construct the Rhombus given the length of side is 5 cm.​

Answer»

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Suppose GIVEN rhombus is ABCD , with each side = 10 cm, smaller DIAGONAL is BD & longer diagonal is AC , with point of intersection O.

TO FIND: AC = ?

< A = 60°

=> TRIANGLE ABD is an equilateral triangle. as AB = AD hence base angles will be equal. & each will be of 60°

Hence smaller diagonal BD = 10 cm => BO = 10/2 = 5 cm

As, diagonals of a rhombus, bisect each other at right angles.

=> TRI AOB is a right triangle with hypotenuse AB.

AB² = BO² + AO²

=> 10² = 5² + AO²

=> AO = √(100 - 25)

=> AO = √75 = 5√3 cm

=> 2AO = 10√3 cm

=> AC = 10√3 cm


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