Question

the area of triangle is 100√3cm². find the perimeter of the triangle

Answer 1

U have to mention the type of triangle . but such questions have equilateral ones . so
ar of eq. triangle = √3/4 .a^2 = 100√3
so a^2/4 = 100 thus a^2 = 400 so a= √400 = 20
so perimeter = 3×20 = 60

Answer 2

 ✬  Perimeter = 60 cm  ✬ 

GIVEN:

• Area of an equilateral triangle = 100√3 cm²

TO FIND:

• What is the perimeter of an equilateral triangle ?

SOLUTION:

Let the side of an equilateral triangle be 'x' cm

✒We know that, the formula for finding the area of an equilateral triangle is :-

✫ Area of an equilateral triangle = √3 $\times$ a²/4 ✫

According to question:-

$\implies$ 100√3 = √3 $\times$ x²/4

$\implies$ 100√3 $\times$ 4= √3x²

$\implies$ 400√3 = √3x²

$\implies$ 400√3/√3 = x²

$\implies$ 400 = x²

$\implies$ √400 = x

$\implies$ 20 cm = x

➱ Side of an equilateral triangle = 20 cm

✒Now, we have to find the perimeter of the triangle

To find the perimeter of the we use the formula:-

✫ Perimeter of triangle = Sum of all sides ✫

【∴ As we know that all sides in equilateral triangle are equal.】

According to question:-

$\implies$ Perimeter = (20 + 20 + 20) cm

$\implies$ Perimeter = 60 cm

❛ Hence, the perimeter of the triangle is 60 cm ❜ 

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✰ Extra Information ✰

➮ All the sides of an equilateral triangle are equal.

➮ The measure of each angle of an equilateral triangle is 60°.

➮ All angles in an equilateral triangle are equal.

➮ Height of an equilateral triangle = √3 $\times$ a/2