millopezle wrote:

Could you please explain how did you get the calculated height of the equilateral triangle in statement 2?

Thanks

hi

millopezleIs the length of a side of equilateral triangle E less than the length of a side of square F?

(1) The perimeter of E and the perimeter of F are equal.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2

since you are asking specific question about statement 2..

it is giving us the ratio of height of triangle E to the diagonal of square F as 2√3 : 3√2...

since its a ratio ,we can multiply both by x, although we dont require that because final answer is also a ratio...

from height of triangle , we can get its side by formula.. h=side1*√3/2...

from diagonal of square we can get side by formula... diagonal=√2*side2

what you require is side1/side2= 2h/√3*dia/√2=2/√6*h/dia=2/√6*2√3/3√2=2/3...

so we have the ratio as 2/3..

so we can say side of square >side of tri... sufficient