Apiece of wire 25 m long is cut into two pieces. one piece is bent into a square and the other is bent into an equilateral triangle.(a) how much wire should be used for the square in order to maximize the total area

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 =

Total area, A = A1 + A2

For maxima and minima, fins dA /dy

It is equal to zero.

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.