Question

Prove that the area of equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.

Answer 1

In`/_ABC`
`AB^2+BC^2=AC^2`
`a^2+a^2=AC^2`
`AC^2=2a^2`
`AC=sqrt2a`
Area of `/_ABE=sqrt3/4a^2`
Area of `/_ACF=sqrt3/4(sqrt2a)^2`
`=2sqrt3/4a^2`
Area of `/_ABE`/area of `/_ACF`=1/2.