Problem Solving

If the ratio between the diagonal of a square and the height of an equilateral triangle is 5/3, respectively, what is the ratio of their areas?

A 5√3/6
B 5√3/18
C 25√3/9
D 25√3/18
E 25/18

Let side of square be a and side of triangle be a'

Ratio of diagonal and height of eq triangle = a√2/ √3a'=> a/a' = 5√3/3√2 = 5√6/6
Squaring both side becomes => a^2/a'^2 = 25/6
Now area of triangle is √3/4 a'^2 so dividing 25/6 by this becomes 100/6√3 = 100√3/18 or 50√3/9 which is not among options.
Please suggest.

Hi prachi,

Let the side of the square = a and the side of the triangle be a'

a√2/ (√3/2)a'=> a/a' = 5√3/6√2 = 5√6/12

Squaring both sides,
a^2/a'^2 = 25/24

Dividing 25/24 by √3/4, we can get the answer to be 25√3/18

other way of solving

side of square = s
side of triangle = a

s root2 /a (root 3)/2 = 5/3
solving
s/a = 5/(2 root6)
s2/a2 = 25/24

area of square/ area of triangle = s2/a2 (root 3)/4

25/(24 * (root 3) /4

25/6 root 3


25 (root 3) / 18