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A triangle with three equal sides has its area equal to 3√3 sq cm. Find its perimeter.
- a)6√3 cm
- b)2√3 cm
- c)5√3 cm
- d)7√3 cm
Correct answer is option 'A'. Can you explain this answer?
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To find the area of a triangle, we can use the formula A = (1/2) * base * height. However, since all three sides of the triangle are equal, we can use a different formula.
Let's denote the length of each side of the triangle as s. According to the given information, the area of the triangle is 3. Since the triangle is equilateral, all three sides have the same length, s.
To find the height of the equilateral triangle, we can use the formula h = (s * √3) / 2. Plugging in the value of s, we get h = (s * √3) / 2.
Now, we can substitute these values into the formula for the area of a triangle:
A = (1/2) * base * height
3 = (1/2) * s * (s * √3) / 2
6 = (s^2 * √3) / 4
24 = s^2 * √3
s^2 = 24 / √3
s^2 = 8√3
Therefore, the length of each side of the equilateral triangle is √(8√3).
Please note that the exact value of √(8√3) cannot be simplified further.
Let's denote the length of each side of the triangle as s. According to the given information, the area of the triangle is 3. Since the triangle is equilateral, all three sides have the same length, s.
To find the height of the equilateral triangle, we can use the formula h = (s * √3) / 2. Plugging in the value of s, we get h = (s * √3) / 2.
Now, we can substitute these values into the formula for the area of a triangle:
A = (1/2) * base * height
3 = (1/2) * s * (s * √3) / 2
6 = (s^2 * √3) / 4
24 = s^2 * √3
s^2 = 24 / √3
s^2 = 8√3
Therefore, the length of each side of the equilateral triangle is √(8√3).
Please note that the exact value of √(8√3) cannot be simplified further.
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A triangle with three equal sides has its area equal to 3√3 sq cm. Find its perimeter.a)6√3 cmb)2√3 cmc)5√3 cmd)7√3 cmCorrect answer is option 'A'. Can you explain this answer?
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