Hello Prasad!

Side of square= a

Diagonal= √2*a

Side of equilateral triangle= a/√2

Area of square= a ²

Area of equilateral triangle= (√3/4)*( a/√2) ² = (√3/8)* a ²

Ratio of area of square to triangle = a ² /(√3/8)* a ² = 8/√3

Hope this helped:)

Hi Prasad!

Let side of equilateral triangle =x

Length of diagonal of square = 2x

Area of square= 1/2 (diagonal 1 )(diagonal 2)

Area of square = 1/2 (2x)²

Area of square = 1/2 (4x²)

Area  of square= 2x²

Find ratio of triangle to square:

triangle : square = √3/4 x² : 2x²

Divide both sides by x²:

triangle : square = √3/4 : 2

Multiply both sides by 4:

triangle : square = √3 : 8

Hope it helped to clear your delimma.

Hello!

Let the diagonal of sq. be '2x' & side of equilateral be 'x' uts.

The side of sq will be (x√2) uts. (By using Pythagoras theorem)

(Side)²+(side)² = (2x)²

Therefore side of sq. Is x√2

Area of square = a² = ( x√2 )² = 2x²

Area of equilateral = √3/4 a² = √3/4 (x²)

Ratio of area of square: area of equilateral triangle = (2x²) ÷ (√3/4 x²) = 8 : √3

i hope this helps.