Video Transcript
Given that ππ squared is equal to 100 square centimeters and π is the midpoint of line segment ππ, determine the length of line segment ππ.
We begin by recalling that taking the square root of a number can be thought of as finding the side length of a square whose area is that number. The question tells us that the square of length ππ is equal to 100 square centimeters and that π is the midpoint of the line segment ππ. We will begin by calculating the length of ππ and then use this to calculate the length of the line segment ππ.
We know that ππ squared is equal to 100. We can take the square roots of both sides of this equation. And since our length must be positive, we have ππ is equal to 10. This means that the length of the line segment ππ is 10 centimeters. As we are told that π is the midpoint of line segment ππ, it follows that the length of line segment ππ is half the length of ππ. One-half of 10 is equal to five, so the length of line segment ππ is five centimeters.