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If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .?
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If the sides of an equilateral triangles are shortened by 3,2,1 respec...
Finding the Side of Equilateral Triangle
Given that by shortening the sides of an equilateral triangle by 3, 2, and 1 respectively, a right-angled triangle is formed, we need to find the side of the equilateral triangle.
Formula for Equilateral Triangle
An equilateral triangle has all its sides equal. Therefore, let's assume that the side of the equilateral triangle is 'x'.
As per the formula for an equilateral triangle,
Perimeter of the equilateral triangle = 3x
Area of the equilateral triangle = (√3/4) x x2
Formation of Right-Angle Triangle
When the sides of the equilateral triangle are shortened by 3, 2, and 1 respectively, a right-angled triangle is formed.
Let's consider the right-angled triangle formed after shortening the sides of the equilateral triangle.
Let the sides of the right-angled triangle be a, b, and c, where c is the hypotenuse.
As per Pythagoras theorem, a2 + b2 = c2
Also, we know that the sides of the right-angled triangle are shortened by 3, 2, and 1 respectively from the sides of the equilateral triangle.
Therefore, a = x - 3, b = x - 2, and c = x - 1.
Substituting the values of a, b, and c in the Pythagoras theorem, we get
(x - 3)2 + (x - 2)2 = (x - 1)2
Solving the above equation, we get
x2 - 8x + 12 = 0
On solving the quadratic equation, we get x = 6.
Conclusion
Therefore, the side of the equilateral triangle is 6 units.
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If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .?
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If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .?.
If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sides of an equilateral triangles are shortened by 3,2,1 respectively then a right angle triangle is formed.what is side of equilateral triangle .?.
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