Question

The area of an equilateral triangle is 100 v3 m. Find the perimeter of the
triangle​

Answer 1

Answer:

Equilateral triangle

Solve for perimeter

P≈45.59

A Area

100

Unit Conversion:

Using the formulas

A=3

4a2

P=3a

Solving forP

P=23¾A=2·3¾·100≈45.59014

Answer 2

• The perimeter of the triangle is 60 m

Given:

The area of the equilateral triangle is 100√3 m sq.

To find:

The perimeter of the equilateral triangle

Something about an equilateral triangle

• All three sides of the equilateral triangle are equal.
• The three interior angles of the equilateral triangle are 60° each.
• The formula to find the area of an equilateral triangle is (√3)/4 * (side)² units sq.

Now,

By using the area formula of the equilateral triangle, we can get the value of the side.

⇒ √3/4 * (side)² = 100√3

⇒ (side)² = 100√3 ÷ √3/4

[By taking √3/4 to RHS]

⇒ (side)² = 100√3 * 4/(√3)

⇒ (side)² = 400

⇒ side = 20 m

[By taking the square roots in both sides]

So,

As each side of an equilateral triangle is the same then, all three sides of the triangle will be 20 m.

Now,

• The perimeter of the equilateral triangle

= sum of all the three sides

= (side) + (side) + (side)

[As all the sides are equal in equilateral triangle]

= 3 * (side)

Then,

= 3 * (20)

= 60 m