GMATPrep Area 1

Question

Please explain:

ps_dahiya · Answer

Area of triangle = t^2 * √3 * 1/2
Area of square = s^2

As given 
s^2 = t^2 * √3 * 1/2
so t^2/s^2 = 4/√3
t/s = 2/  4  √3

haas_mba07 · Answer

Area of equilateral triangle = t^2 x sqrt(3)/4

Area of square = s^2

Take ratio of t/s from t^2/s^2 and simplify... 2: (3^1/4)

heman · Answer

Height of triangle^2 + t^2/4 = t^2 
Height of triangle^2 = t^2 - t^2/4
 = 3t^2/4
 Height = t sqrt(3)/2

Area of triangle = 1/2* t* t sqrt(3)/2
 = t^2*sqrt(3)/4

Area of square = s^2

t^2*sqrt(3)/4 = s^2

t^2/s^2 = 4/sqrt(3)

t/s = 2/ (3)^1/4

Hence D
Heman

GMATT73 · Answer

How did you get from t^2*sqrt3/2=s^2 ---> t^2/s^2=4/√3 :?:

I get 2/√3 for the RHS

Futuristic · Answer

D for me.

t^2/s^2 = 4/3^0.5

jamesrwright3 · Answer

I am confused on the math

jamesrwright3 · Answer

I understand how you get the t^2/s^2 on the left side, but how does the sqrt3*1/2 become 4/sqrt 3 on the right hand side?

jamesrwright3 · Answer

Ok I start out like this

s^2=t^2(sqrt 3)/4

Basically I get 

4/sqrt 3=t^2/s^2

How do I get it into the form of answer D?
Can someone help me?

Jim

Futuristic · Answer

t/s = sqrt (4/sqrt(3))
= sqrt(4)/sqrt(sqrt(3))
=2/(3^0.5)^0.5

Now,
(a^b)^c = a^(bc)
=>
(3^0.5)^0.5 = 3^(0.5 x 0.5) = 3^0.25

Makes sense?

jamesrwright3 · Answer

Totally confused still:( 
How can I get the answer from the way I was doing it
I know it's right. 
I have the t over the s and didn't violate any rules of algebra
Any suggestions?

sgrover · Answer

You were doing the right thing.
t^2/s^2 = 4/(3^1/2)
To find t/s, take the square root on both sides.

t/s = (4^1/2)/((3^1/2)^1/2)
 = 2/(3^1/4)

which is (D)

ps_dahiya · Answer

Actually its a typo.
Read s^2 = t^2 * √3 *  1/2 

As
s^2 = t^2 * √3 *  1/4 

To speedup the things, remember
1. Area of a equilateral triangle of side t = t^2 * √3 * 1/4
2. Area of a triangle inscribed in a circle is r^2 * 3*SQRT(3)/4 where r is the radius of circle. Area of triangle is 41.3% of the area of circle.
3. Area of a circle, when the side of triangle inscribed in that circle is x, will be (PI * x^2) /3
4. Area of a square inscribed in a circle is 2* r^2 where r is the radius of circle. Area of triangle is approx 63.66% of the area of circle.

GMATT73 · Answer

Thanx. Now the problem makes a lot more sense. 

BTW: Those are some useful formulas to save a tremendous amount of time.

GMATPrep Area 1

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