Problem Solving

There is an equilateral triangle with side t and a square with side s.

If the triangle and the square have the same area, what is the ratio t:s?

2:3
16:3
4:sq.rt3
2:sq.rt3(actually its a sq.rt 3 with a 4 on the root symbol)

Ans D

Money man, you've only include 4 of the answer choices.

Area of triangle A1 = sqrt(3/4) * t^2
Area of Square A2 = s^2
A1 = A2
hence t:s = (2/sqrt(sqrt(3))
Ans. D ....

I have included four choices but I have included the right answer in it..just a lil lazy to type..sorry..

I still dint understand the explanation given though...can someone else offer their views pls..Stuart pls help!!

Moneyman,

You first have to know the following formula for the area of an equilateral triangle:

area = s^2 * sqroot3/4, where s is a measure of a side of the triangle.

Since you are told that the side of a triangle is t, you just square the t and get:

t^2sqroot3/4

The formula for the area of a square is easy enough: side squared.

s^2

Now, you are told that the two areas equal to one another.

The tricky part is to follow algebra without pulling a silly mistake:

s^2 = t^2 sqroot3/4 [multiply both sides by 4]

4s^2 = t^2 sqroot3 [divide both sides by s^2]

4 = t^2 sqroot3/s^2 [multiply both sides by 1/sqroot3]

4/sqroot3 = t^2/s^2 [get rid of the squares by sqroot-ing both sides]

sqroot4/sqroot of sqroot3 = t/s

2/sqroot of sqroot3 = t/s [here is where a lot of people make the mistake, they reduce the two sqroots and get 2:3, which is WRONG]

sqroot of 3 is actuall 3 taken to the power of one half [1/2]

the sqroot sign has a 2 that we do not write because it is such a common operation [for example you do write the 3 when you take a cube root of something]

Therefore, when you see a sqroot of a sqroot of 3, it is really:

sqroot3^(1/2) the two in the denominator is then multiplied by the "invisible" 2 in the sqroot sign, yielding a 4.

Hope this helps.

Sorry I didn't help you before, I was being an ass.

Thanks AleksandrM!!