CAT 2018 Question Paper Shift 1 Solved Paper

Question : 87 of 100

Marks: +1, -0

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joiningthe midpoints of the sides of T1. Then a third triangle T3 is formed by joining themidpoints of the sides of T2. If this process of forming triangles is continued, the sum ofthe areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will be

192 $√3$
188 $√3$
164 $√3$
248 $√3$

Validate

Solution:

Any equilateral triangle formed by joining the midpoints of the sides of another equilateral triangle will have its side equal to half the side of the second equilateral triangle.
Side of

{T} 1=24 {cm}

Side of

{T} 2=12 {cm}

Side of

{T} 3=6 {cm}

and so on.
Sum of the areas of all the triangles

=\;{√{3}}/{4}(24^{2}+12^{2}+6^{2}+. . . . . .)

=\;{√{3}}/{4}(\;{576}/{1-\;{1}/{4}})=192 √{3}

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