Latest Elitmus Aptitude Question SOLUTION: from an equilateral triangle with area 3 units, new triangle is formed using the midpoints of each side.the process continues indefinitly for the newly formd equltrl triangle.what

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(#M40037657) ELITMUS Numerical Ability question geometry Keep an EYE

from an equilateral triangle with area 3 units, new triangle is formed using the midpoints of each side.the process continues indefinitly for the newly formd equltrl triangle.what is the sum of areas of all trinagls

Asked In Elitmus TONU (9 years ago)

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smi  (9 years ago)

Area of equilateral triangle=3units
Now midpoints are joined to form new equilateral traingle area becomes 1/4 th of the orginal one..
Hence the process continues to infinity
Therefore,
3+3*1/4+3*1/16+.... to infinity
This is the sum of an infinite gp wid common ration=1/4
Sum of all such areas= 3/(1-1/4)=3*4/3=4 units

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RAHUL KUMAR  (9 years ago)

ans = 4 unit
area of equilateral triangle= 3 unit
when we form a new triangle using the mid point of each side then the area of new triangle will be =area of original triangle/4
similarly for 2nd form triangle area=area of original triangle/4^2
this process continue till infinity
so sum of area of all formed triangle=3+(3/4)+(3/4^2)+............
=3(1/(1-1/4))
=3*4/(4-1)
=4unit

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