Latest TCS Aptitude Question SOLUTION: The diagonal of a square is twice the side of equilateral triangle the ratio of Area of the Triangle to the Area of Square is? a) √3:8 b) √2:5 c) √3:6 d) √2:4

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The diagonal of a square is twice the side of equilateral triangle the ratio of Area of the Triangle to the Area of Square is?
a) √3:8 b) √2:5 c) √3:6 d) √2:4

Asked In TCS krishnamurthy (11 years ago)

Unsolved Read Solution (11)

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lala  (11 years ago)

let side of square is a
then diagonal of square is {sqrt2a}
given {sqrt2a}= 2*side of triangle
so side of triangle = {sqrt2a}/2 i.e a/sqrt2
area of triangle = sqrt3/4*side^2......according to formula
new area = sqrt3/4*{a/sqrt2}*{a/sqrt2} i.e.........sqrt3a*a/8
area of square = a^2
ratio = sqrt3*a^2/8a^2....i.e sqrt3/8

Is this solution Helpfull? Yes (55) | No (3)  

Abhishek kUNDU  (11 years ago)

is it 2012 tcs recent paper???

Is this solution Helpfull? Yes (19) | No (10)  

chandrakant   (11 years ago)

sqrt3 :8
triangle area=sqrt3/4*a^2
square area=2a^2

Is this solution Helpfull? Yes (5) | No (9)  

yasaswini  (11 years ago)

diagonal of a square is 2a
area of the square=1/2*(diagonal)^2 i.e 2a^2
side of the equi triangle is a
area of equi triangle=(3/4)a^2
3/4a^2:2a^2
3:8

Is this solution Helpfull? Yes (5) | No (18)  

Harsha  (9 years ago)

Let the side of equilateral triangle = 1 unit.
We know that area of an equilateral triangle =root3/a^2
As side = 1 unit area of the equilateral triangle =root3/4
Now Diagonal of the square = 2 (side of the equilateral triangle) = 2
We know that area of the square =half D^2 where D = diagonal
So area of the square =half * 2^2=2
Ratio of the areas of equilateral triangle and square = (root3/4):(2)
=root3 :8

Is this solution Helpfull? Yes (2) | No   

shivaram akumalla  (8 years ago)

√3/4*(a)^2:1/2*(2a)^2
Thus √3:8

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Anubhav Rajvanshi  (8 years ago)

area of equilateral triangle is sqrt3/4a^2
assume side of equilateral triangle be 3
thus diagonal of square is 6
area of equialteral triangle is 9*sqrt3/4
area of square is 1/2*diagonal^2=18
9*sqrt3/4:18
sqrt3/4:2
sqrt3:8
option a is the answer

Is this solution Helpfull? Yes (1) | No   

narendra  (7 years ago)

diagnol of a square=sqt2*a
let "b" be the side of equilateral triangle
therefore, sqrt2*a=2*b ==>a=sqrt b
therfore : area of equilateral triangle/area of square=sqrt3 :8 is the final answer

Is this solution Helpfull? Yes (1) | No   

Rahul Sinha  (7 years ago)

(a) is correct option
ans = sqrt(3) a^2 / 2 a^2
= sqrt(3)/8

Is this solution Helpfull? Yes (1) | No   

N.Sowjanya  (7 years ago)

assume side of square is x1 and side of equilateral triangle is x2
diagonal of the square is square root of 2(x1)
sqrt(2)(x1)=2(x2)
(3)^(12)4(x2)^2:x2^2
substitute x2 value in terms of x1
and the answer is 'a'

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Arunava Samanta  (1 year ago)

The length of a diagonal of a square is a*sqrt(2) , where a= side of a square
According to the question, the diagonal of a square is twice the side of equilateral triangle
therefore, The side of this triangle is half of a*sqrt(2)
So, Area of a Equilateral Triangle is {sqrt(3)/4} * (a/sqrt(2))^2

ratio is -----> {sqrt(3)/4} * (a/sqrt(2))^2 : a^2
=> sqrt(3)/8 : 1
=> sqrt(3) : 8 (answer is option a)

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