gnr646 wrote:

If the area of an equilateral triangle with side t is equal to the area of a square with side s, what is the ratio of t to s?

a) 2:3

b) 16:3

c) 4:(3^1/2)

d) 2:(3^1/4)

e) 4:(3^1/4)

I get D.

I first tried numbers but this wasnt getting me anywhere.

So I just used variables. A of T=b*h/2. A of S: S1*S2.

in this case A of the triangle is: 1/2t*1/2tsqrt3. The reason its 1/2sqrt3 is because when u split a equilateral into two it becomes to 30-60-90 triangles. the base corresponds to angle 30 and is 1/2t. So the height is 1/2tsqrt3.

A of the square is just s*s=s^2.

make the equations equal to eachother. s^2=1/2t*1/2tsqrt3. --> s^2=1/4t^2sqrt3. Sqrt both sides. --> s=1/2t *3^1/4.

t/s=1/2*3^1/4---> 2/3^1/4.