Question

# Find the perimeter and height of an equilateral triangle whose area is equal to 60cm^{2}

Hint:

## The correct answer is: 12√15 cm

### It is given that area of an equilateral triangle = 60 cm^{2}

Area of equilateral triangle = (side)^{2}

Let side of the triangle = a

⇒ (side)^{2} = 60

⇒ (a)^{2} = 4 60 = 240

⇒ a =

⇒ a = 4 cm

We know all the angles of an equilateral triangle are equal i.e. 60° each.

Let height of the triangle = h

Sin A = =

Sin 60° =

6 = h

So, height of the triangle = 6 cm

Since all the sides of an equilateral triangle are equal,

Perimeter = 3 side = 3 4 cm

= 12 cm

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