# Biggie Size It!

By Page Bird

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.

Using GSP I constructed a triangle.  I then doubled the sides to create a similar triangle with twice the perimeter as seen below.

Using GSP, I created the following tables for the perimeter and area of the triangles above:

So when you double the perimeter of a triangle, the area increases four times.

How would the results change if you triple the lengths of each of the sides?

Again, I used GSP to create a triangle three times the size of the original triangle as shown below:

Using GSP I created tables of both the perimeters and the areas:

So the when the perimeter is tripled the area increases nine times.

Based on these two cases, it seems that when the perimeter is increased n times, then the area will increase by n2 .  Using GSP, I will test this for n = 10.  So when the perimeter is increased by 10 times then the area will increase by 100 times.

As predicted, the tables show that when the perimeter is increased ten times the area increases 100 times.