# Activities

• • • ##### Subject Area

• Math: Geometry: Reasoning

• ##### Author 6-8
9-12

• ##### Activity Time

30-45 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• TI-Navigator™
• ##### Other Materials
Graph paper for each student or a worksheet with the rectanles already drawn
• ##### Report an Issue

Perimeter of a Rectangel with Fixed Area

#### Activity Overview

Students will investigate the relationship between the base of a rectangle with area of 35 or 36 and its perimeter.

#### Before the Activity

Prepare the Activity Center with the desired windows 0

#### During the Activity

Assign each pair of students one of the following numbers: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, or 18. Have them draw a rectangle with that number for a base and having an area of 35 or 36.(or provide a worksheet with rectangles already drawn).
Have the students calculate (or measure) the height of the rectangle and its perimeter. The students can either enter their base and perimeter as a point to contribute to TI-Navigator™, or the teacher can call on students to randomly to submit their points to an overhead calculator.
Do a scatter plot of the data. Talk about calculating the height by dividing 36 by the base. Take the perimeter formula and substitute x for the length and 36/x for the width in P= 2(l + w) to get P=2(x + 36/x).
Show that when you enter y=2(x+36/x) the line hits all of the points.

#### After the Activity

Ask the students to look at the graph and tell the minimum value for the perimeter.

• What value of the base gives this value?