Answer:
10.87 m
Explanation:
Total length of the wire = 25 m
Let the length of one piece is y and other piece is 25 - y
Let the side of square is a.
So, 4 a = y
a = y / 4
And the side of triangle is b
3 b = (25 - y)
b = (25 - y) / 3
Area of square, A1 = side x side =
A1 = y² / 16
Area of equilateral triangle, A2 = [tex]\frac{\sqrt{3}}{4}\times b^{2}[/tex]
[tex]A_{2}=\frac{\sqrt{3}}{4}\frac{\left ( 25-y \right )^{2}}{9}[/tex]
Total area, A = A1 + A2
[tex]A=\frac{y^{2}}{16}+\frac{\sqrt{3}}{4}\frac{\left ( 25-y \right )^{2}}{9}[/tex]
For maxima and minima, fins dA /dy
[tex]\frac{dA}{dy}=\frac{y}{8}-\frac{1.732}{18} \times \frac{25-y}{1}[/tex]
It is equal to zero.
[tex]\frac{y}{8}=\frac{1.732}{18} \times \frac{25-y}{1}[/tex]
9y = 173.2 -6.928 y
15.928 y = 173.2
y = 10.87 m
So, the length of wire to make square is 10.87 m.
