Question

a rhombus of side 14cm has one angle equal to 60°. Find the lengths of the diagonals of the rhombus.​

Answer 1

Answer:

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