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Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will be
  • a)
    188√3
  • b)
    248√3
  • c)
    164√3
  • d)
    192√3
Correct answer is option 'D'. Can you explain this answer?

Answers

We can see that T2 is formed by using the mid points of T1. Hence, we can say that area of triangle of T2 will be (1/4)thof the area of triangle T1.
Area of triangle T1 =√3 / 4 * (24)2 = 144√3 sq.cm
Area of triangle T2 = 144√3 / 4= 36√3 sq. cm
Sum of the area of all triangles = T1 + T2 + T3 + ...
=>T1 + T1 /4 + T1 /42 + ...
=> T1 / 1 – 0.25
=>4 / 3 * T1
=>4 / 3 * 144√3
=>192 √3
Hence, option D is the correct answer.

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Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer?.
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Here you can find the meaning of Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will bea)188√3b)248√3c)164√3d)192√3Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
We can see that T2 is formed by using the mid points of T1. Hence, we can say that area of triangle of T2 will be (1/4)thof the area of triangle T1.Area of triangle T1 =√3 / 4 * (24)2 = 144√3 sq.cmArea of triangle T2 = 144√3 / 4= 36√3 sq. cmSum of the area of all triangles = T1 + T2 + T3 + ...=>T1 + T1 /4 + T1 /42 + ...=> T1 / 1 – 0.25=>4 / 3 * T1=>4 / 3 * 144√3=>192 √3Hence, option D is the correct answer.