The sum of the perimeter of a equilateral triangle and square is 10. Find the dimensions of the triangle of and square that produce a minimum total area.

My Work:

Perimeter of square is 4x.

Perimeter of Equilateral is 3y.

Area of square is x^2.

Area of Equilateral triangle is [y^2*sqrt(3)]/4.

Total area is x^2 + [y^2*sqrt(3)/4].

Total perimeter is 3y + 3x, where 3y + 4x = 10.

I then solved 10 = 3y + 4x for y and got y = (10-4x)/3.

Afterward, I plugged y into the total perimeter.

Let T = total perimeter

T = x^2 + (1/4)[(10-4x)/3]^2*sqrt(3).

I then found T prime.

T' = 2x + (2x-5)/3*sqrt(3)

Let T' = 0 to find x.

I found out that x = 5/[6*sqrt(3) + 2]

I stopped here because it does not make sense to me.

Can someone get me started in the right direction?