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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2, Problem 24P

**(a)**

To determine

**To find:** The function that models the total area enclosed by two squares.

Expert Solution

The function that models the area of both the squares is

**Given:**

Length of wire is

Length of first wire after cutting is *x* and length of second wire is

**Calculation:**

If length of wires are

Total enclosed area

Where,

Area of a square is,

Where, *l* is side of square.

Substitute *l* in above equation (2) for area

The area enclosed by square of side

Substitute

The total area is calculated as follows,

Further solving,

Thus, the function that models the area of both the squares is

**(b)**

To determine

**To find:** The value of

Expert Solution

The value of *x* that minimizes the area of the square is 5 cm.

Function that models the area of square as calculated in part (a) is

Sketch the function

From the above figure, it can be observed that the function has minimum value at

Therefore, for the area to be minimum the length of the first wire must be 5 cm.