Question

a piece of wire 10m long is cut into two pieces. one piece is bent into a square andthe other is bent into an equilateral triangle. how should the wire be cut so that the total areaenclosed is maximum? minimum?

Answer 1

To maximize the total area enclosed, the wire should be cut in such a way that the square and the triangle have equal perimeters.

Step-by-step explanation:

To maximize the total area enclosed, the wire should be cut in such a way that the square and the equilateral triangle have equal perimeters. Let's denote the length of the square side as 'x' and the length of the triangle side as 'y'. Since the wire is 10m long, we have x + y = 10.

The perimeter of a square is 4x and the perimeter of an equilateral triangle is 3y. To maximize the area, the perimeters should be equal, so 4x = 3y. We can solve this system of equations to find the values of x and y that maximize the area enclosed.