Question

perimeter of rhombus is 80 CM. one pair of opposite angle is 60° each. find digonals.​

Answer 1

Rhombus
Solve for perimeter
P=4a

Answer 2

Answer:

20 cm and 20√3 cm

Step-by-step explanation:

Perimeter = 80cm

So, one side = 80/4 = 20 cm

Now, the shorter diagonal and any two sides (better draw the diagram to understand this) will form an equilateral triangle, as one angle is 60 degrees and the adjacent sides are equal. Hence opposite angles are also equal, i.e., 60 degrees.

Therefore, the shorter diagonal = 20 cm.

We know, the diagonals of a rhombus bisect each other at right angles.

So, as per Pythagoras' theorem,

(half of shorter diagonal)^2 + (half of longer diagonal)^2 = (side of rhombus)^2

{again refer to the diagram that you have drawn}.

So, 10^2 = (half of longer diagonal)^2 = 20^2

Longer diagonal = 2*[√(400-100)] = 20√3 cm.