Problem Solving Set #3

October 15, 2010
Question 8
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  d)60  e)100

To solve this problem I found the perimeter of the triangle by 20+20+20= 60, since all sides are equal because it's an equilateral triangle.  Since the square has the same perimeter of 60 and it has four equal sides to find the side length you do the following equation 60/4= 15.  If a square has a side length of 15 you'd use the equation 15² = 225 to find the area of the square.  Therefore the area of the square is c)225.

This question is interesting because it shows how different shapes with the same perimeter can have vastly different areas.  For example an equilateral triangle with a side length of 20 would have an area of around 86.6 square units, whereas the square has 225 square units.  I find this rather fascinating.

In solving this problem I have discovered that problems are easy to solve when you follow logical steps and know your formulas.