To find: The function that models the total area enclosed by two squares.
The function that models the area of both the squares is .
Length of wire is .
Length of first wire after cutting is x and length of second wire is .
If length of wires are and then length of side of square is and .
Total enclosed area by both the squares is,
Where, is total enclosed area, is area of square whose side is and is area of square whose side is .
Area of a square is,
Where, l is side of square.
Substitute for l in above equation (2) for area ,
The area enclosed by square of side is .
Substitute for in equation (2) for area ,
The total area is calculated as follows,
Thus, the function that models the area of both the squares is .
To find: The value of such that area enclosed by the two squares is minimum.
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 using graphing calculator as shown below.
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.
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