Question

perimeter of rhombus is 80cm one pair of opposite angle is 60 degree each find diagonal ​
.plz explanation.​​

Answer 1

GIVEN:

Perimeter of the rhombus is 80 cm and one of the angles is 60°

CONCEPT:

All the sides of the rhombus are equal always.

If the angle between two equal sides of a triangle is 60° then third side will also be equal to those 2 sides.

FORMULA USED:

Perimeter of the rhombus = 4 × Side

Area of equilateral triangle = 4 × (Side)2

CALCULATION:

Perimeter of the rhombus = 80 cm

∴ Side of the rhombus = 80/4 = 20 cm

Now,

One of the angles is 60° and adjacent sides are equal in the rhombus.

So, the adjacent side will form an equilateral triangle with the diagonal.

Hence,

Area of the rhombus = Area of 2 equilateral triangles whose sides are 20 cm

∴ Area of the rhombus = 2 × √3/4 × 20 × 20 = 10 × 20 × 1.73 = 346 cm2