Question

The area of an equilateral triangle is 36 × √(3 ) sq.cm. What is the length of each side? *
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Answer 1

Answer:

The answer will be 12 cm.

Step-by-step explanation:

We have given;

Area of equilateral triangle = 36 * √(3);

Now, we know that area of equilateral triangle is given as;

= (√3) * a^2 / 4; ( derived from Heron's formula) (i)

Hence, from given things and equation (i), it can be deduced that;

= (√3) * a^2 / 4 = 36 * √(3);

= a^2 / 4 = 36;

= a^2 = 36 * 4;

= a = √(36*4);

= a = 6 *2;

= a = 12;

( 'a' was the side of equilateral triangle in the formula)

Hence, the side of equilateral triangle measures 12 cm.

That's all.

Answer 2

It is given that the area of an equilateral triangle is 36√3 cm².

We need to find the length of each side of the triangle.

A triangle is a 2 - dimensional shape. An equilateral triangle is a triangle with all three sides of equal measure, as the sides are equal all three internal angle must be equal. So, an equilateral triangle is a regular polygon of 3 sides.

Solution:

Let the side of the equilateral triangle be "s"

The area of an equilateral triangle with each side of measure "s" is given by this formula:

√3/4 ( s² )

Area = √3/4 ( s² )

⟹ 36√3 cm² = √3/4 ( s² )

⟹ 36√3 cm² × 4 = √3( s² )

⟹ 36 cm² × 4 = √3(s²) / √3

⟹ 36 cm² × 4 = s²

⟹ 144 cm²= s²

⟹ √(144 cm²) = s

⟹ 12 cm = s

12 cm is the the side of an equilateral triangle that has an area of 36√3 cm²

Double check:

Area = √3/4 ( s² )

⟹ 36√3 cm² = √3/4 ( 12 cm )²

⟹ 36√3 cm² = √3/4 × 144 cm²

⟹ 36√3 cm² = 36√3 cm²

LHS = RHS

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