Problem Solving

If two regions (one a triangle with equals sides, T, and a square with side,S) have the same area, what is the ratio of T:S?

2:3
16:3
4: sq rt of 3
2: 4th rt of 3
4: 4th rt of 3


Answer is D......

PLEASE TELL ME WHERE I WENT WRONG....

I made both areas equal to 36. Obviously S will be 6 and T works out to be 6 sq rt 2. IS THIS RIGHT? If so, how do I translate this into the the correct answer?

Areas are equal
sqrt3*(T^2)/4 = S^2
T/S = 2/ 4th rt 3

Could you explain a little bit further? I kinda know how you got sq rt of 3 but please explain your math.....

THANKS...

i think you could solve this problem algebrically than picking the numbers.

the triangle mentioned in the problem is an equvilateral triangle with side T and the area of an eq. triangle is

[(square root of 3)*T^2]/4

and the area of a square with side S = S^2

given that area of eq. triangle = area of square


[(square root of 3)*T^2]/4 = S^2
rearranging the variables,
(T/S)^2 = 4:(square root of 3)

or (T/S) = (2: 4th root of 3)

answer D

The formula for calculating the Area of the equilateral triangle is
root3*side^2/4

sqrt3*(Tri Side^2)/4 = Squ side^2
sqrt3*(Tri Side^2) = 4 * Squ side^2
(Tri Side^2) / Squ side^2 = 4/sqrt3

taking root on both sides

Tri side/Squ side = 2/ 4th rt 3

Hope that helps....

It does help. I had no idea there was a standard formula for the area of an equallateral triangle.

I figured it out by working it out. 1/2* T/2 * T sq rt 3. Is that correct?

Thanks guys.