# Optimization expression Problem

## Homework Statement

Hello,

Can you help me to understand the question..Ineed clarification and hints to solve the question..

A circle and a square are to be constructed from a piece of a wire of length l.

1-give an expression for the total area of the square and circle formed.

2-find the radius of the circle and side of the square that make their areas equal.

3-find values of the radius of the circle and side of the square which give the largest and smallest total area.

4-If insted of the circle another square is formed.Find the values of the sides of the square that yeild the largest and smallest total area.

## The Attempt at a Solution

I solve (1) & (2) but I have difficulties on (3) &(4)

1-give an expression for the total area of the square and circle formed.

we assume that :

length of wire=circumference of circle+perimeter of square

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Area of square= a^2

*To know the length of side of square:

perimeter of square=4*a

a= perimeter/4

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Area of square= a^2

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Area of circle=pi*r^2

r= circumference of circle / 2 PI

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Total Area=Area of square +Area of circle

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2-find the radius of the circle and side of the square that make their areas equal.

Area of square=Area of circle :

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The value of radius and side of square :

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