The length of each side of an equilateral triangle having an area of 9√3 cm² is
a. 8 cm
b. 36 cm
c. 4 cm
d. 6 cm

Solution:

Given, the area of an equilateral triangle is 9√3 cm²

We have to find the length of each side of an equilateral triangle

Area of an equilateral triangle = √3/4 (side)²

9√3 = √3/4 (side)²

9 = 1/4 (side)²

(side)² = 9(4)

(side)² = 36

Taking square root,

Side = 6 cm

Therefore, the length of each side of an equilateral triangle is 6 cm.

✦ Try This: The length of each side of an equilateral triangle having an area of 4√3 cm² is

Given, the area of an equilateral triangle is 4√3 cm²

We have to find the length of each side of an equilateral triangle

Area of an equilateral triangle = √3/4 (side)²

4√3 = √3/4 (side)²

4 = 1/4 (side)²

(side)² = 4(4)

(side)² = 16

Taking square root,

Side = 4 cm

Therefore, the length of each side of an equilateral triangle is 4 cm.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12

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NCERT Exemplar Class 9 Maths Exercise 12.1 Problem 5

The length of each side of an equilateral triangle having an area of 9√3 cm² is a. 8 cm, b. 36 cm, c. 4 cm, d. 6 cm

Summary:

In geometry, a triangle with all equal sides is said to be an equilateral triangle. The length of each side of an equilateral triangle having an area of 9√3 cm² is 6 cm

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