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Find the length of each side of an equilateral triangle having area of 9 root 3 cm square
- a)36 cm
- b)5 cm
- c)15 cm
- d)6 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the length of each side of an equilateral triangle having area of...
Given area of equilateral triangle = 9√3 cm²
Also,
Area of the equilateral triangle = √3/4 × (side)²
So,
√3/4 × (side)² = 9√3
side² = (9√3 × 4)/√3
side² = 36
side = √36
side = 6cm
Also,
Area of the equilateral triangle = √3/4 × (side)²
So,
√3/4 × (side)² = 9√3
side² = (9√3 × 4)/√3
side² = 36
side = √36
side = 6cm
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Find the length of each side of an equilateral triangle having area of...
To find the length of each side of an equilateral triangle, we need to use the formula for the area of an equilateral triangle. The formula is:
Area = (sqrt(3) / 4) * s^2
Where 's' is the length of each side of the equilateral triangle.
Given that the area is 9√3 cm², we can substitute this value into the formula and solve for 's'.
1. Substitute the given values into the formula:
9√3 = (sqrt(3) / 4) * s^2
2. Simplify the equation:
Multiply both sides of the equation by 4 to get rid of the fraction:
36√3 = sqrt(3) * s^2
3. Square both sides to eliminate the square root:
(36√3)^2 = (sqrt(3) * s)^2
1296 * 3 = 3 * s^2
3888 = 3 * s^2
4. Divide both sides by 3 to isolate s^2:
3888 / 3 = s^2
1296 = s^2
5. Take the square root of both sides to find the length of each side:
s = sqrt(1296)
s = 36
Therefore, the length of each side of the equilateral triangle is 36 cm.
Area = (sqrt(3) / 4) * s^2
Where 's' is the length of each side of the equilateral triangle.
Given that the area is 9√3 cm², we can substitute this value into the formula and solve for 's'.
1. Substitute the given values into the formula:
9√3 = (sqrt(3) / 4) * s^2
2. Simplify the equation:
Multiply both sides of the equation by 4 to get rid of the fraction:
36√3 = sqrt(3) * s^2
3. Square both sides to eliminate the square root:
(36√3)^2 = (sqrt(3) * s)^2
1296 * 3 = 3 * s^2
3888 = 3 * s^2
4. Divide both sides by 3 to isolate s^2:
3888 / 3 = s^2
1296 = s^2
5. Take the square root of both sides to find the length of each side:
s = sqrt(1296)
s = 36
Therefore, the length of each side of the equilateral triangle is 36 cm.
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Find the length of each side of an equilateral triangle having area of 9 root 3 cm squarea)36 cmb)5 cmc)15 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the length of each side of an equilateral triangle having area of 9 root 3 cm squarea)36 cmb)5 cmc)15 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the length of each side of an equilateral triangle having area of 9 root 3 cm squarea)36 cmb)5 cmc)15 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer?.
Find the length of each side of an equilateral triangle having area of 9 root 3 cm squarea)36 cmb)5 cmc)15 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the length of each side of an equilateral triangle having area of 9 root 3 cm squarea)36 cmb)5 cmc)15 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the length of each side of an equilateral triangle having area of 9 root 3 cm squarea)36 cmb)5 cmc)15 cmd)6 cmCorrect answer is option 'D'. Can you explain this answer?.
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