Problem Set Number 3

Question: An equilateral triangle has a side length of 20. If a square has the same perimeter as this triangle, the area of the square is:
a) 25  b)400  c)225  e)100

An equilateral triangle means that the sides are all the same length. If one of these side lengths is 20, then the perimeter of the triangle is 60. (20+20+20=60) A square has four sides all the same length. If the perimeter of the square is 60, then each side is 15. (60/4=15) To find the area of a square, the formula is S^2 where S is the side length. 15^2=225. Therefore, the area of the square is 225 making the answer c.

I like this question because it is simple, but it is a good example of how different shapes with the same perimeter don't necessarily have the same area. We shouldn't just assume things. We might assume that the area of these two shapes is the same because the perimeter is the same. As shown in this question, the area can be very different.

I have learned that problem solving is much easier when you completely understand the question. If you do not fully understand a question, it is easy to assume things and make "silly" mistakes. It is also important to read and reread a question to make sure that you didn't miss anything.

JJXN