Latest CDS Aptitude Question SOLUTION: A square and an equilateral triangle have same perimaters. If the diagonal of the square is 12 sqrt 2 cm then what is the area of the triangle ?

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A square and an equilateral triangle have same perimaters. If the diagonal of the square is 12 sqrt 2 cm then what is the area of the triangle ?

Asked In CDS Devendra Marghade (11 years ago)

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Susanta Kar  (11 years ago)

When 'a' is the side of a square then its diagonal is a*sqrt(2).

Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.

Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm

Side of triangle = perimeter/3 = 48/3 = 16cm

Area of equilateral triangle = sqrt(3)/4*(side of triangle)^2 = sqrt(3)/4*16^2
= sqrt(3)/4*256 = 64*sqrt(3) sq.cm.(ans)

Is this solution Helpfull? Yes (6) | No (1)  

PARAG KAMRA  (11 years ago)

When 'a' is the side of a square then its diagonal is a*sqrt(2).

Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.

Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm

Side of triangle = perimeter/3 = 48/3 = 16cm

Altitude of equilateral triangle = sqrt(3)/2*side of triangle sqrt(3)/2*16 = 8*sqrt(3) cm

Area of triangle = (1/2)*16*8*sqrt(3) = 64*sqrt(3) sq.cm.(ans)

Is this solution Helpfull? Yes (2) | No   

bagavath  (10 years ago)

if diagonal of a square is a*sqrt(2) means then side is a.
therefore, the side of the square is 12 cm. area of the triangle is a^2*(sqrt(3)/4). so answer is 64sqrt(3) sq.cm.

Is this solution Helpfull? Yes (2) | No   

PARAG KAMRA  (11 years ago)

When 'a' is the side of a square then its diagonal is a*sqrt(2).

Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.

Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm

Side of triangle = perimeter/3 = 48/3 = 16cm

Altitude of equilateral triangle = 1/2*side of triangle =(1/2)*16 = 8cm

Area of triangle = (1/2)*16*8 = 64 sq.cm.(ans)

Is this solution Helpfull? Yes (1) | No (3)  

yeginati haribabu  (11 years ago)

When 'a' is the side of a square then its diagonal is a*sqrt(2).

Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.

Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm

Side of triangle = perimeter/3 = 48/3 = 16cm

Area of equilateral triangle = sqrt(3)/4*(side of triangle)^2 = sqrt(3)/4*16^2
= sqrt(3)/4*256 = 64*sqrt(3) sq.cm.(ans)

Is this solution Helpfull? Yes (1) | No   

sowmya  (9 years ago)

20/100=0.2
0.2*20=4

Is this solution Helpfull? Yes (1) | No   

jagannathan  (11 years ago)

PERIMETER OF SQUARE=PERIMETER OF EQ.TRIANGLE
4A=3L. DIAGONAL 0F SQUARE=12SQ.RT2=SQ.RT(A^2+A^2)
SQ.RT(2)A=12.SQ.RT(2)=>A=12. PERIMETER OF STRIANGLE=48.L=16.
AREA OF TRIANGLE=1/2(B*H)=(1/2)*16*(SQ.RT(432))

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jitendra kumar  (10 years ago)

a=12
perimeter of square=48
therefore side of traingle is 16
area of traingle is 1.732 *64 cm^2

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nipun yadav  (10 years ago)

When 'a' is the side of a square then its diagonal is a*sqrt(2).

Hence, side of square will be 12 cm if its diagonal is 12*sqrt(2) cm.

Perimeter of triangle = perimeter of square = 4*side = 4*12 = 48cm

Side of triangle = perimeter/3 = 48/3 = 16cm

Altitude of equilateral triangle = sqrt(3)/2*side of triangle sqrt(3)/2*16 = 8*sqrt(3) cm

Area of triangle = (1/2)*16*8*sqrt(3) = 64*sqrt(3) sq.cm.(ans)

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Ajay Kumar Gupta  (9 years ago)

144 cm^2.
area(triangle)=area(square)
diagonal of square=12 sqrt 2=(side length) sqrt 2
i.e,side length of square=12 cm
so area of square=12^2=144 cm^2=area(triangle)

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HARSHWARDHAN  (9 years ago)

let side of square & triangle be a and b resp.
A.T.Q , 4a=3b
diagonal of square=a*sqrt(2) which is given as 12*sqrt(2)
so, a=12 => b=16
so, area of triangle equals sqrt(3)*16*16/4=64*sqrt(3) sq.cm (ans)

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Pooja bala singh  (9 years ago)

Answer will be 36^1/2

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