Area of the equilateral triangle = (t^2)*(1/4)*(sqrt3) and the area of the square = s^2

equating the two, t^2(sqrt3)/4 = s^2 hence (t/s)^2 = 4/sqrt(3) or t/s = (4/3^(1/2))^(1/2)

which seems complicated but in fact comes to t/s = 2/(3)^1/4

Hope it helped.

I suggest that you search the question first before you post,

https://www.beatthegmat.com/areas-and-ratios-t29764.html

papgust wrote:I suggest that you search the question first before you post,

https://www.beatthegmat.com/areas-and-ratios-t29764.html

Hi Papgust,
Actually, I did it, for the last posts ... anyway I'm going to check the other posts ...

Thanks mj78ind for your quick answer.

Silvia.

Hi Silvia,

You may find it worthwhile to memorize the formula for the area of an equilateral triangle of side t. The area is t^2*root(3)/4. We're told that this area is the same as the area of the square (s^2). Thus we can equate the two values and manipulate the equation until we isolate t/s.

If you perform the simplification correctly, you will find that t/s equals answer D. This is the OA.

A detailed step-by-step solution, a 30-second hack, and a video solution are available at GMATPrep Question 1111. To practice similar questions, set topics='Geometry' and difficulty='700+' in the Drill Generator

Hope you kick butt tomorrow!
-Patrick