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

Given that (π‘‹π‘Œ)Β² = 100 cmΒ² and 𝑍 is the midpoint of line segment π‘‹π‘Œ, determine the length of line segment 𝑋𝑍.

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Video Transcript

Given that π‘‹π‘Œ squared is equal to 100 square centimeters and 𝑍 is the midpoint of line segment π‘‹π‘Œ, determine the length of line segment 𝑋𝑍.

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‘Œ is equal to 100 square centimeters and that 𝑍 is the midpoint of the line segment π‘‹π‘Œ. We will begin by calculating the length of π‘‹π‘Œ and then use this to calculate the length of the line segment 𝑋𝑍.

We know that π‘‹π‘Œ 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‘Œ is equal to 10. This means that the length of the line segment π‘‹π‘Œ is 10 centimeters. As we are told that 𝑍 is the midpoint of line segment π‘‹π‘Œ, it follows that the length of line segment 𝑋𝑍 is half the length of π‘‹π‘Œ. One-half of 10 is equal to five, so the length of line segment 𝑋𝑍 is five centimeters.

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