Ratio of the area of a square to the area of a triangle

[kevin]

What is the ratio of the area of a square of side 5 to an equilateral triangle with sides of 5? Doesn't seem like a hard question, but the given answer is 4sqrt(3)/3.

Any ideas on how to get to this final answer?


Thanks

[little_dragon]

What is the ratio of the area of a square of side 5 to an equilateral triangle with sides of 5? Doesn't seem like a hard question, but the given answer is 4sqrt(3)/3.

wat areas did U get? wat did U get when U divided?

[kevin]

I got 25 for the area of the square and the triangle I got 6.25

[maggiemagnet]

I got 25 for the area of the square and the triangle I got 6.25

You shouldn't have gotten an exact decimal value for the triangle, so something went wrong there. Please reply showing your steps, starting with finding the altitude of the equilateral triangle (possibly using the ratios for a 30-60-90 triangle, which is half of an equilateral). Thanks!

[monkeyolsen]

area of square = 5*5 = 25

Triangle

altitude:
let the altitude of the equilateral triangle be x
5^2 = (2.5)^2 + x^2
x^2 = 25-(25/4)
= 75/4
x = 5root(3)/2

area of triangle = (b*h)/2
b = 5
h= x = 5root(3)/2

area = [(5)*(5root(3)/2)]/2
= 25root(3)/4

ratio of area of square to area of triangle = 25/[25root(3)/4]
= [25*4]/[25 root(3)] = 4/[root(3)]

multiply top and bottom by [root(3)]
4*root(3)/[root(3)*root(3)] = 4root(3)/3