Lesson 3

Each of the rectangles in the image has something in common with the other rectangles. Can you guess what that is?

In this Math Lab activity you will confirm your hypothesis and discover an interesting aspect of design.

Problem

For a rectangle with constant perimeter, what dimensions of the rectangle will give you the maximum area?

Consider the problem; then write down a hypothesis.

Procedure

Use Rectangle Drawer to construct rectangles of different shapes.

Analysis

1. What dimensions of a rectangle give you the maximum area?
   
   
2. Assume that a rectangle has an area of 306 cm2. The perimeter of the rectangle is 70 cm. Determine the dimensions of the rectangle by
   
   
   1. using Rectangle Drawer
      
      
   2. solving a quadratic equation

Save your work in your course folder.

Keep your answers to this Math Lab handy. You will revisit the ideas developed here later in the lesson.