Well, we do not know the formula for equilateral triangle.
Let's find the formula of the area of the triangle first.
Draw the high of the triangle. You have 2 right triangles. You have the hypothenuse t and half of the base 1/2t. You know that triangle which are 30°-60°-90° have side ratios like that x:xsqrt(3):2x
2x is the hypothenuse and here we have t, so x=t/2 so the ratios of this triangle are
1/2*t : 1/2*t*sqrt(3) : t
You know have the base and the height of the triangle so its area is
(t*1/2*t*sqrt(3))/2= t²*(sqrt(3)/4)
Now we can put
t²*(sqrt(3)/4)=s²
t²*sqrt(3)=s²*4
sqrt both sides
t*(3^1/4)=s*2
t*(3^1/4)/s=2
t/s=2/3^1/4
A little long.
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geometry
Source: Beat The GMAT — Problem Solving |
area of square = s^2
area of equilateral triangle = t^2 *(sqrt3)/4
s^2 = t^2 *(sqrt3)/4
4*s^2= t^2 sqrt3
sqrt (4*s^2/sqrt3 ) = t
2s /(4root3) = t
2s = 4root3 t
2:4root3
Hence D.
area of equilateral triangle = t^2 *(sqrt3)/4
s^2 = t^2 *(sqrt3)/4
4*s^2= t^2 sqrt3
sqrt (4*s^2/sqrt3 ) = t
2s /(4root3) = t
2s = 4root3 t
2:4root3
Hence D.
Area of equvilateral triangle is sqrt 3/4a^2superrrom wrote:got confused with this one. Thanks
area of a square is S^2
therefore its
sqrt3/4 *(t)^2 = s^2
rt 3*t^2 = 4*s^2
square rooting on both sides we get
t*4th root 3 = 2 S
there fore ratio of t:s is
2: 4throot 3
hope it helps
