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The length of the sides of a triangle are 2x y/2, 5x/3 y 1/2 and 2x/3 2y 5/2. If the triangle is equilateral, find its perimeter?
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The length of the sides of a triangle are 2x y/2, 5x/3 y 1/2 and...
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The length of the sides of a triangle are 2x y/2, 5x/3 y 1/2 and...
Given
- Length of first side: 2x y/2
- Length of second side: 5x/3 y 1/2
- Length of third side: 2x/3 2y 5/2
- The triangle is equilateral
Solution
For an equilateral triangle, all three sides are equal in length. Therefore, we can set the length of the first side equal to the length of the second side and the length of the third side:
2x y/2 = 5x/3 y 1/2 = 2x/3 2y 5/2
To solve for x and y, we can use any two of the equations:
2x y/2 = 5x/3 y 1/2
=> 12x 3y = 10x 9y 3/2
=> 2x = 3y 3/4
2x y/2 = 2x/3 2y 5/2
=> 12x 3y = 4x 12y 15
=> 8x = 9y 5
Solving these equations simultaneously, we get:
x = (45/62)y
Substituting this value of x in any of the equations, we can solve for y:
2x y/2 = 5x/3 y 1/2
=> 62y/31 y/2 = 75y/62 y 1/2
=> y = 31/2
Therefore, the length of each side of the equilateral triangle is:
2x y/2 = 2(45/62)(31/2)/2 = 45/31
The perimeter of the triangle is:
3(45/31) = 135/31
Answer
The perimeter of the equilateral triangle is 135/31.
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The length of the sides of a triangle are 2x y/2, 5x/3 y 1/2 and 2x/3 2y 5/2. If the triangle is equilateral, find its perimeter?
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The length of the sides of a triangle are 2x y/2, 5x/3 y 1/2 and 2x/3 2y 5/2. If the triangle is equilateral, find its perimeter? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of the sides of a triangle are 2x y/2, 5x/3 y 1/2 and 2x/3 2y 5/2. If the triangle is equilateral, find its perimeter? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the sides of a triangle are 2x y/2, 5x/3 y 1/2 and 2x/3 2y 5/2. If the triangle is equilateral, find its perimeter?.
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