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If an equilateral triangle of area X and a square of area Y have the same perimeter, then :
- a)X > Y
- b)X = Y
- c)X < Y
- d)X < Y
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If an equilateral triangle of area X and a square of area Y have the s...
Given:
- An equilateral triangle of area X
- A square of area Y
- Both have the same perimeter
To find:
The relationship between X and Y
Solution:
Let's consider the properties of the equilateral triangle and the square.
Equilateral Triangle:
- All three sides are equal in length
- The sum of the angles is 180 degrees
- The area of an equilateral triangle is given by the formula: Area = (√3/4) * side^2
- The perimeter of an equilateral triangle is given by the formula: Perimeter = 3 * side
Square:
- All four sides are equal in length
- All angles are right angles (90 degrees)
- The area of a square is given by the formula: Area = side^2
- The perimeter of a square is given by the formula: Perimeter = 4 * side
Given that the equilateral triangle and the square have the same perimeter:
3 * side (equilateral triangle) = 4 * side (square)
Dividing both sides by side, we get:
3 = 4
This implies that the sides of the equilateral triangle and the square are in the ratio of 4:3.
Relationship between the areas:
Let's assume the side of the equilateral triangle is 4x and the side of the square is 3x (where x is a constant).
- The area of the equilateral triangle, X = (√3/4) * (4x)^2 = 4√3x^2
- The area of the square, Y = (3x)^2 = 9x^2
Therefore, we can conclude that:
X : Y = 4√3x^2 : 9x^2
Simplifying further:
X : Y = 4√3 : 9
Hence, the correct answer is option C: X < y.="" />
- An equilateral triangle of area X
- A square of area Y
- Both have the same perimeter
To find:
The relationship between X and Y
Solution:
Let's consider the properties of the equilateral triangle and the square.
Equilateral Triangle:
- All three sides are equal in length
- The sum of the angles is 180 degrees
- The area of an equilateral triangle is given by the formula: Area = (√3/4) * side^2
- The perimeter of an equilateral triangle is given by the formula: Perimeter = 3 * side
Square:
- All four sides are equal in length
- All angles are right angles (90 degrees)
- The area of a square is given by the formula: Area = side^2
- The perimeter of a square is given by the formula: Perimeter = 4 * side
Given that the equilateral triangle and the square have the same perimeter:
3 * side (equilateral triangle) = 4 * side (square)
Dividing both sides by side, we get:
3 = 4
This implies that the sides of the equilateral triangle and the square are in the ratio of 4:3.
Relationship between the areas:
Let's assume the side of the equilateral triangle is 4x and the side of the square is 3x (where x is a constant).
- The area of the equilateral triangle, X = (√3/4) * (4x)^2 = 4√3x^2
- The area of the square, Y = (3x)^2 = 9x^2
Therefore, we can conclude that:
X : Y = 4√3x^2 : 9x^2
Simplifying further:
X : Y = 4√3 : 9
Hence, the correct answer is option C: X < y.="" />
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Community Answer
If an equilateral triangle of area X and a square of area Y have the s...
Area of equilateral triangle = √3/4×(side)^2
Area of square = (side)^2
X is equal to area of equilateral triangle
Y is equal to area of square
so always
[√3/4×(side)^2]< />
Hence X
Area of square = (side)^2
X is equal to area of equilateral triangle
Y is equal to area of square
so always
[√3/4×(side)^2]< />
Hence X
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If an equilateral triangle of area X and a square of area Y have the same perimeter, then :a)X > Yb)X = Yc)X < Yd)X <YCorrect answer is option 'C'. Can you explain this answer?
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If an equilateral triangle of area X and a square of area Y have the same perimeter, then :a)X > Yb)X = Yc)X < Yd)X <YCorrect answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If an equilateral triangle of area X and a square of area Y have the same perimeter, then :a)X > Yb)X = Yc)X < Yd)X <YCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an equilateral triangle of area X and a square of area Y have the same perimeter, then :a)X > Yb)X = Yc)X < Yd)X <YCorrect answer is option 'C'. Can you explain this answer?.
If an equilateral triangle of area X and a square of area Y have the same perimeter, then :a)X > Yb)X = Yc)X < Yd)X <YCorrect answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If an equilateral triangle of area X and a square of area Y have the same perimeter, then :a)X > Yb)X = Yc)X < Yd)X <YCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an equilateral triangle of area X and a square of area Y have the same perimeter, then :a)X > Yb)X = Yc)X < Yd)X <YCorrect answer is option 'C'. Can you explain this answer?.
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