Question

Question #5777d

Answer 1

The area of a square is more than a triangle if the perimeter is same.

Explanation:

Let the perimeter be 'x'
In case of square:- 4 * side = x. so, side = x/4
Then area of square =`(side)^2 = (x/4)^2 = (x^2)/16`
suppose it is equilateral triangle:- Then 3 * side = x
so, side = x/3. hence area = `[sqrt3 * (side)^2]/4 = [sqrt3 * (x/3)^2]/4` =`[x^2.sqrt3]/36`
Now comparing square to triangle
`x^2/16 : [x^2 *sqrt3]/36 = 9:4sqrt3` = 9 : 4*1.732 = 9 : 6.928
obviously area of square is more than the triangle.