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.
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.
