the side of a rhombus is 3m and one angle is 60 degree. what is the sum of its diagonals.
Answers
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
Answer:
Sum of the diagonals=3(1+√3) m or 3(1+1.73)=3(2.73)=8.19 m (approximately).
Step-by-step explanation:
Used concept:-
Properties of Rhombus:-
All sides of the rhombus are equal.
The opposite sides of a rhombus are parallel.
Opposite angles of a rhombus are equal.
In a rhombus, diagonals bisect each other at right angles.
Diagonals bisect the angles of a rhombus.
The sum of two adjacent angles is equal to 180 degrees.
