by what the length of each side of an equilateral triangle with an area of 9/3cm be?
( 8 cm
(i) 36 cm
(ii) 4 cm
(i) 6 cm
Answers
Given:
✰ Area of an equilateral triangle = 9√3 cm²
To find:
✠ The length of each side of an equilateral triangle.
Solution:
Equilateral triangle:
An equilateral triangle is the one in which all sides of the triangle are equal.
This question is from the topic the concept of measurement. We will use the formula of area of an equilateral triangle, as we are provided with the area of an equilateral triangle. Putting the values in the formula and then doing the required calculations, we will find its side of an equilateral triangle.
Let's find out...✧
✭ Area of an equilateral triangle = √3/4 ×a²✭
Where,
a is the length of each side of an equilateral triangle.
Putting the values in the formula, we have:
➤ √3/4 × a² = 9√3
➤ a² = 9√3 × 4/√3
Now, √3 in numerator and √3 in denominator gets cancel, we have:
➤ a² = 9 × 4
➤ a² = 36
➤ a = √36
➤ a = 6 cm
∴ The length of each side of an equilateral triangle = 6 cm
What if we need to find perimeter of triangle also?
As it is later triangle so we will just multiply 3 by its side. As the triangle is an enclosed figure of three sides and an equilateral triangle all sides are equal.
Therefore,
➤ Perimeter of triangle = 3 × its side
➤ Perimeter of triangle = 3 × 6
➤ Perimeter of triangle = 18 cm
∴ The perimeter of an equilateral triangle = 18 cm
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