Intermath | Workshop Support

Write-up


Title
Biggie Size This

Problem Statement
 

If you double the lengths of each of the sides of a triangle, what happens to the perimeter and the area? Explain why.

How would the results change if you triple the lengths of each of the sides? What if you make the sides ten times their original size? Explain your reasoning.


Problem setup

This problems asks us to double the sides of a triangle and compare the related perimeters and areas. As a further investigation, we are asked to triple the sides, quadruple the sides, etc….

 

Plans to Solve/Investigate the Problem

To begin I drew similar triangles in GeoSketchPad. I drew one with a k value of 2/1 and a third with a k value of 3/1. I then created an Excel spreadsheet with k values from 2 to 10..

 

Investigation/Exploration of the Problem

Upon finishing my GeoSketchPad drawings, I calculated the perimeters and areas. As you will see below, as the perimeters increased by a rate of k+1, the areas increased by (k+1)². When I entered the data into an Excel spreadsheet, this held true throughout each k. See Below:

 

 

 

Side A

Side B

Side C

S

Perimeter

Area

P ratio

A Ratio

 

2

3

4

4.5

9

2.904738

 

 

 

4

6

8

9

18

11.61895

 1/2

 1/4

 

6

9

12

13.5

27

26.14264

 1/3

 1/9

 

8

12

16

18

36

46.4758

 1/4

0.0625

 

10

15

20

22.5

45

72.61844

 1/5

0.04

 

12

18

24

27

54

104.5706

 1/6

0.027778

 

14

21

28

31.5

63

142.3321

 1/7

0.020408

 

16

24

32

36

72

185.9032

 1/8

0.015625

 

18

27

36

40.5

81

235.2837

 1/9

0.012346

 

20

30

40

45

90

290.4738

0.1

0.01

 

 

 

 

 

 

 

 

 

 

 

 

Author & Contact
Jim Taylor
jtaylor1@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials