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Given an equilateral triangle T1 with side 24 cm | Quantitative Aptitude - Geometry – Mensuration

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Mensuration: Given an equilateral triangle T1 with side 24 cm. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2018 - Slot-1 - Geometry - Question-5 - Given an equilateral triangle T1 with side 24 cm

Q. 5: 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?
1. 164√3
2. 188√3
3. 248√3
4. 192√3

Correct Answer: 4. 192√3

As P,Q and R are mid points of AC,AB and BC so both triangle PQR and CBA will be similar and PQ = BC/2

So if the area of triangle ABC = A then area of triangle PQR = A/4

Thus

Sum of Areas = A+A/4+A/16+A/64+ ——–=A/(1-1/4)=4/3 A=4/3×√3/4×24^2=192√3

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