Question Video: Solving Word Problems Involving Square Roots in a Geometric Context Mathematics • 8th Grade

Given that (ππ)Β² = 100 cmΒ² and π is the midpoint of line segment ππ, determine the length of line segment ππ.

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Video Transcript

Given that ππ squared is equal to 100 square centimeters and π is the midpoint of line segment ππ, determine the length of line segment ππ.

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 ππ is equal to 100 square centimeters and that π is the midpoint of the line segment ππ. We will begin by calculating the length of ππ and then use this to calculate the length of the line segment ππ.

We know that ππ 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 ππ is equal to 10. This means that the length of the line segment ππ is 10 centimeters. As we are told that π is the midpoint of line segment ππ, it follows that the length of line segment ππ is half the length of ππ. One-half of 10 is equal to five, so the length of line segment ππ is five centimeters.