Math CentralQuandaries & Queries


Subject: mathematic question
Name: mohammad
Who are you: Student

determine the maximum area of a rectangle with each perimeter to one decimal place?
a)100 cm b)72 m c)169 km d)143 mm

Hi Mohammad,

This is like making a rectangular garden by first putting a fence around it. You have purchased some fencing that will form the perimeter of the rectangle and you want to know how long and wide to make the garden so that it has the largest area possible. The area of a rectangle is the length times the width and with the given amount of fencing you have you get the maximum area if the length and width are equal, that is the shape of the garden is a square.

I am going to illustrate with anexample. Suppose I have 38 m of fencing to enclose my rectangular garden. To have a maximum area the rectangle must be a square, that is each of the 4 sides have the same length. Thus the length of a side is 38/4 = 9.5 m. The area of the garden is then

length × width = 9.5 × 9.5 = 90.25 square metres.

To one decimal place that's 90.3 square metres.

Now try the perimeters given in your problem,

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