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A square is made by joining the mid-points of the sides of the larger square. There is circle inscribed in the smaller square and an equilateral triangle inscribed in the circle. Find the ratio of the side of larger square to the side of the equilateral triangle?
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A square is made by joining the mid-points of the sides of the larger ...
Solution:
Let's assume that the side length of the larger square is 'a'.
Step 1: Finding the side length of the smaller square
To find the side length of the smaller square, we use the property that the mid-point of a side of a square divides the side into two equal parts.
Since the mid-points of the sides of the larger square are joined to form the smaller square, the side length of the smaller square is half the side length of the larger square.
Therefore, the side length of the smaller square is 'a/2'.
Step 2: Finding the radius of the circle
Since the circle is inscribed in the smaller square, the radius of the circle is half the side length of the smaller square.
Therefore, the radius of the circle is 'a/4'.
Step 3: Finding the side length of the equilateral triangle
To find the side length of the equilateral triangle, we use the property that in an equilateral triangle, the radius of the inscribed circle is equal to the height of the triangle.
The height of an equilateral triangle is given by the formula h = √3/2 * s, where s is the side length of the triangle.
Since the radius of the circle is 'a/4', we can equate it to the height of the equilateral triangle:
a/4 = √3/2 * s
Simplifying the equation, we find:
s = (2a/4) * (2/√3)
s = a/√3
Step 4: Finding the ratio
The ratio of the side length of the larger square to the side length of the equilateral triangle can be found by dividing the two:
Ratio = (a) / (a/√3)
Ratio = √3
Therefore, the ratio of the side length of the larger square to the side length of the equilateral triangle is √3.
Let's assume that the side length of the larger square is 'a'.
Step 1: Finding the side length of the smaller square
To find the side length of the smaller square, we use the property that the mid-point of a side of a square divides the side into two equal parts.
Since the mid-points of the sides of the larger square are joined to form the smaller square, the side length of the smaller square is half the side length of the larger square.
Therefore, the side length of the smaller square is 'a/2'.
Step 2: Finding the radius of the circle
Since the circle is inscribed in the smaller square, the radius of the circle is half the side length of the smaller square.
Therefore, the radius of the circle is 'a/4'.
Step 3: Finding the side length of the equilateral triangle
To find the side length of the equilateral triangle, we use the property that in an equilateral triangle, the radius of the inscribed circle is equal to the height of the triangle.
The height of an equilateral triangle is given by the formula h = √3/2 * s, where s is the side length of the triangle.
Since the radius of the circle is 'a/4', we can equate it to the height of the equilateral triangle:
a/4 = √3/2 * s
Simplifying the equation, we find:
s = (2a/4) * (2/√3)
s = a/√3
Step 4: Finding the ratio
The ratio of the side length of the larger square to the side length of the equilateral triangle can be found by dividing the two:
Ratio = (a) / (a/√3)
Ratio = √3
Therefore, the ratio of the side length of the larger square to the side length of the equilateral triangle is √3.
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A square is made by joining the mid-points of the sides of the larger square. There is circle inscribed in the smaller square and an equilateral triangle inscribed in the circle. Find the ratio of the side of larger square to the side of the equilateral triangle?
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A square is made by joining the mid-points of the sides of the larger square. There is circle inscribed in the smaller square and an equilateral triangle inscribed in the circle. Find the ratio of the side of larger square to the side of the equilateral triangle? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about A square is made by joining the mid-points of the sides of the larger square. There is circle inscribed in the smaller square and an equilateral triangle inscribed in the circle. Find the ratio of the side of larger square to the side of the equilateral triangle? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square is made by joining the mid-points of the sides of the larger square. There is circle inscribed in the smaller square and an equilateral triangle inscribed in the circle. Find the ratio of the side of larger square to the side of the equilateral triangle?.
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