If a square with side length 54 centimeters has the same perimeter as an equilateral triangle, what is the side length of the triangle?
Let’s start this question by modeling our square. A square is a four-sided polygon that has all interior angles equal and four sides of the same length. We’re told in the question that this square has a side length of 54 centimeters. We’re then told that there’s an equilateral triangle. This will be a triangle that has three sides of the same length. We don’t know the length of one of the sides of the triangle, and indeed that’s what we’re asked to find out.
The only other piece of information we’re given is that the square and the triangle have the same perimeter. Let’s see if we can find the perimeter of the square and use this to help us find the side length of the triangle. Sometimes we can get confused between area and perimeter, but we can recall that the perimeter is the distance around the outside edge. We need to add up all of the lengths on the outside edge. We can remember that the square has all four sides the same, so we’ll have four lots of 54 centimeters.
When we multiply four by 54, we get a perimeter of 216 centimeters. So now we know that this triangle will have the same perimeter of 216 centimeters. We can denote the side length of one of these sides to be 𝑥 centimeters. Adding the three lengths of 𝑥 centimeters would give us three 𝑥 centimeters, and we can write that that’s equal to 216. We now need to solve this to find the value of 𝑥. Dividing both sides of this equation by three, we calculate 216 divided by three, which would give us that 𝑥 is equal to 72 centimeters.
As we define the side length of the triangle to be 𝑥, then we find that the side length of this equilateral triangle will be 72 centimeters.