triangle and square

Question

An equilateral triangle with a side length of t and a square with a side length of s have equal areas.

what is t/s?

correct anwer: 2/(3^1/4)

would very much appreciate if somebody provided an explanation for this question..

bschool2014 · Answer

Area of triangle = (3^1/2)/4 t ^2

Area of Square = s^2

We have,

t^2/s^2 = 4/(3)^0.5

=> t/s = 2/(3)^0.25

tt2011 · Answer

then you are assuming that the height splits the side which it is perpendicular to into 2 equal segments, each t/2 long..then using hypotenuse theorem you arrive at the length of height..thanks

jamifahad · Answer

Area of equilateral triangle =  \sqrt{3}/4 (side)^2  (memorize it!)
= \sqrt{3}/4 * t^2 
Area of square = (side)^2 =  s^2

Area of equilateral triangle=Area of square
= \sqrt{3}/4 * t^2=s^2 
 t^2/s^2 = 4/\sqrt{3} 
 t/s = 2/(sqrt(\sqrt{3})) 
 t/s = 2/3^(1^/^4)

aks1985 · Answer

I'm guessing since this is a GMAT Prep question the area of a equilateral triangle is expected to be memorized?

aks1985 · Answer

I don't quiet get how you get from

= \sqrt{3}/4 * t^2=s^2 
 t^2/s^2 = 4/\sqrt{3}

could you simplify for dummies. Thanks

meshell · Answer

\sqrt{3}/4 * t^2 = s^2

1. moving the fraction to the other side of the equation you will multiply by its reciprocal (as it would have changed the sign from multiply to divide when it crossed the equal sign), so we get

t^2 = s^2 * 4/\sqrt{3}

2. then you move the s^2 over to join the t^2, and as it is multiplied on its original side it will flip its sign to division, so you get

t^2 / s^2 = 4 / \sqrt{3}

once we're there, you want to get rid of the squares on t and s , so you use square root throughout the equation, which will cancel out the squares on t and s on the left, and  \sqrt{4}  becomes 2 and the square root of  \sqrt{3}  doubles the root, so its the 4th root of 3, which the gmat just to get the last twist in, then put in fractional exponent form, which is 3^1/4.

t/s = 2/3^1/4

Spidy001 · Answer

area of a equilateral triangle with side 't' = (sqrt(3)/4)*t^2

area of a square with side s = s^2

as the areas are same

(sqrt(3)/4)*(t^2) = s^2

=> s/t =  4/ (3^(1/4)

triangle and square

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