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Solve the following question and mark the best possible option.
A square, S1, circumscribes the circumcircle of an equilateral triangle of side 10 cm. A square, S2, is inscribed in the incircle of the triangle. What is the ratio of the area of S1 to the area of S2?
  • a)
    4 : 1
  • b)
    32 : 1
  • c)
    8 : 1
  • d)
    2 : 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Solve the following question and mark the best possible option.A squar...
Option 3
The height of the equilateral triangle is 5√3 cm.
Since the height is also the median, we know that the circum-radius is 2/3 × 5√3 = 10√3/3 and the in-radius is 1/3 × 5√3 = 5√3/3.
The diameter of the circumcircle is the side of square S1.
So the area of S1 is (2 × 10√3/3)2 = 1200/9.
The diameter of the in-circle is the diagonal of square S2.
So the area of S2 is ½ × (2 × 5√3/3)2 = 300/18.
Thus the ratio of areas S1 : S2 is 1200/9 : 300/18 = 8 : 1.
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Most Upvoted Answer
Solve the following question and mark the best possible option.A squar...
Option 3
The height of the equilateral triangle is 5√3 cm.
Since the height is also the median, we know that the circum-radius is 2/3 × 5√3 = 10√3/3 and the in-radius is 1/3 × 5√3 = 5√3/3.
The diameter of the circumcircle is the side of square S1.
So the area of S1 is (2 × 10√3/3)2 = 1200/9.
The diameter of the in-circle is the diagonal of square S2.
So the area of S2 is ½ × (2 × 5√3/3)2 = 300/18.
Thus the ratio of areas S1 : S2 is 1200/9 : 300/18 = 8 : 1.
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Community Answer
Solve the following question and mark the best possible option.A squar...
Option 3
The height of the equilateral triangle is 5√3 cm.
Since the height is also the median, we know that the circum-radius is 2/3 × 5√3 = 10√3/3 and the in-radius is 1/3 × 5√3 = 5√3/3.
The diameter of the circumcircle is the side of square S1.
So the area of S1 is (2 × 10√3/3)2 = 1200/9.
The diameter of the in-circle is the diagonal of square S2.
So the area of S2 is ½ × (2 × 5√3/3)2 = 300/18.
Thus the ratio of areas S1 : S2 is 1200/9 : 300/18 = 8 : 1.
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Solve the following question and mark the best possible option.A square, S1, circumscribes the circumcircle of an equilateral triangle of side 10 cm. A square, S2, is inscribed in the incircle of the triangle. What is the ratio of the area of S1 to the area of S2?a)4 : 1b)32 : 1c)8 : 1d)2 : 1Correct answer is option 'C'. Can you explain this answer?
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