SSC CGL Exam > SSC CGL Questions > A square is made by joining the mid-points of...
Start Learning for Free
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?
- a)(2√2)/3
- b)√2/√3
- c)(4√2)/√3
- d)(2√2)/√3
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A square is made by joining the mid-points of the sides of the larger ...
Let the side length of the larger square be $s$, and let the side length of the smaller square be $x$. The diagonal of the smaller square is the side length of the larger square, so by Pythagoras, $x^2+x^2=s^2$, or $2x^2=s^2$. Taking the square root of both sides, we have $x=\frac{s}{\sqrt{2}}$.
The circle inscribed in the smaller square has its center at the center of the square, and its radius is half the side length of the square, so the radius is $\frac{x}{2}=\frac{s}{2\sqrt{2}}$.
The equilateral triangle inscribed in the circle has its circumradius equal to the radius of the circle. The formula for the circumradius of an equilateral triangle with side length $a$ is $R=\frac{a}{\sqrt{3}}$. In this case, the radius of the circle is $\frac{s}{2\sqrt{2}}$, so the side length of the equilateral triangle is $a=R\sqrt{3}=\frac{s}{2\sqrt{2}}\sqrt{3}=\frac{s\sqrt{3}}{2\sqrt{2}}=\frac{s\sqrt{6}}{4}$.
Therefore, the ratio of the side length of the larger square to the side length of the equilateral triangle is $\frac{s}{\frac{s\sqrt{6}}{4}}=\frac{4}{\sqrt{6}}=\boxed{\frac{2\sqrt{6}}{3}}$.
The circle inscribed in the smaller square has its center at the center of the square, and its radius is half the side length of the square, so the radius is $\frac{x}{2}=\frac{s}{2\sqrt{2}}$.
The equilateral triangle inscribed in the circle has its circumradius equal to the radius of the circle. The formula for the circumradius of an equilateral triangle with side length $a$ is $R=\frac{a}{\sqrt{3}}$. In this case, the radius of the circle is $\frac{s}{2\sqrt{2}}$, so the side length of the equilateral triangle is $a=R\sqrt{3}=\frac{s}{2\sqrt{2}}\sqrt{3}=\frac{s\sqrt{3}}{2\sqrt{2}}=\frac{s\sqrt{6}}{4}$.
Therefore, the ratio of the side length of the larger square to the side length of the equilateral triangle is $\frac{s}{\frac{s\sqrt{6}}{4}}=\frac{4}{\sqrt{6}}=\boxed{\frac{2\sqrt{6}}{3}}$.
Free Test
FREE
| Start Free Test |
Community Answer
A square is made by joining the mid-points of the sides of the larger ...
Let the side of larger square = 2a
Side of smaller square = √(a²+a²) = √a a
Radius of circle = (√a a)/2 = a/√a
Let side of triangle be ‘x’ Radius of circumcircle of triangle = x/√3
Therefore; x/√3 = a/√2 a/x = √2/√3 2a/x = (2√2)/√3
Attention SSC CGL Students!
To make sure you are not studying endlessly, EduRev has designed SSC CGL study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in SSC CGL.
|
Explore Courses for SSC CGL exam
|
|
Similar SSC CGL Doubts
Top Courses for SSC CGLView all
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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer?
Question Description
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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer?.
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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer?.
Solutions 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
Here you can find the meaning of 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer?, a detailed solution 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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?a)(2√2)/3b)√2/√3c) (4√2)/√3d)(2√2)/√3Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice SSC CGL tests.
|
|
Explore Courses for SSC CGL exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup