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Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.
An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?
- a)
- b)
- c)
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Directions: In a square of side 10 m, an isosceles triangle is placed...
Looking at the conditions given in the question we can analyze three phases of the same. Firstly, we focus on the original square and the isosceles triangle inscribed inside it. Second we focus on the square which is inscribed in the smallest portion and the three compartments it creates. Thirdly, the entire focus is on the equilateral triangle and visualizing the distance required to find.
Let x be the length of the square as shown above. We can clearly see, that triangle FGH and triangle AHI are similar to each other. The lines FD and HI are parallel to each other and by AA similarity we can prove it.
FG = 2.5-x, HI=x, GH = x, AI = 10-x
(2.5 - x)(10 - x) = x
25 - 12.5x + x2 = x
12.5x = 25
X = 2
The length of the square is two, then in the figure 2 above,
Smallest area = 1/2 × (2.5-x)× x = 1/2 ×0.5 × 2 = 0.5 ..(i)
Area of square = 4 ..(ii)
Largest area = 1/2 × (10-x)×2 = 10-x = 8 ..(iii)
Let the vertex of triangle inside the square be O.
Length of the side of square = length of the side of equilateral triangle
In the figure three we see that OH is the required length
OH2 = OJ2 + HJ2
HJ = 1/2
x = 1 m
OJ = x - height of equilateral triangle
Height of equilateral triangle =
OJ = 2-√3
OH2 = (2-√3)2 + 12
OH = 
OH is the required distance as calculated above.
Hence, the correct option is (a).
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Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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ample number of questions to practice Directions: In a square of side 10 m, an isosceles triangle is placed on one of the sides of the square. The base of the triangle is half of the side, while it has the maximum possible height. The triangle creates few portions in the square. A smaller square is placed in the smallest portion with one vertex touching the triangle. The smaller portion now has three compartments because of the square.An equilateral triangle is placed in the smaller square, with its base coinciding with one of the sides of the square. What is the distance of the vertex of the triangle inside the square from one of the corners of the square (other than the corners of the base side)?a)b)c)d)None of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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