Refer to Exercise 31a to obtain the figure.
Refer to Exercise 31a.
The figure obtained is as shown.
Form an expression for the width of the rectangle.
The perimeter of the figure is the sum of the lengths of the rectangle and the circumference of the circle. So,
Therefore, an expression for the width
of the rectangle is
Substitute 30 for
in the expression for the width of the rectangle.
To complete six rows of the given table, first choose a value for
, say 30.
So, the width of the rectangle is
m when its length is 30 m.
Multiply the length and the width of the rectangle.
The area of a rectangle is the product of its length and width.
So, to find the area of the rectangle when its length is 30m, multiply 30 by
Organize the results in the third row of the table.
Repeat the above procedure for three more values of
Next, repeat the above procedure for three more values of
, say 40, 50 and 60.
The completed table is as shown.
Observe the table.
The area increases till the length of the rectangle is 50 m and then decreases.
So, the maximum area of the rectangular region is approximately 1592 m
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