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

Given that (𝑋𝑌)² = 100 cm² and 𝑍 is the midpoint of line segment 𝑋𝑌, determine the length of line segment 𝑋𝑍.

01:38

### Video Transcript

Given that 𝑋𝑌 squared is equal to 100 square centimeters and 𝑍 is the midpoint of line segment 𝑋𝑌, 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 𝑋𝑌 is equal to 100 square centimeters and that 𝑍 is the midpoint of the line segment 𝑋𝑌. We will begin by calculating the length of 𝑋𝑌 and then use this to calculate the length of the line segment 𝑋𝑍.

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