Question
Use the figure below for questions 9 - 9. If \( D F=61 \) and \( E F=18 \), find \( D E \).
Ask by Mcguire Savage. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( D E = 43 \)
Solution
To determine \( D E \) given that \( D F = 61 \) and \( E F = 18 \), we'll assume that points \( D \), \( E \), and \( F \) are collinear (lying on a straight line).
Here's how to approach the problem:
1. **Understand the Positions:**
- If \( D \), \( E \), and \( F \) are on a straight line, and \( D \) is at one end, \( F \) is at the other end, and \( E \) is somewhere in between, then:
\[
D F = D E + E F
\]
2. **Plug in the Known Values:**
- Given \( D F = 61 \) and \( E F = 18 \):
\[
61 = D E + 18
\]
3. **Solve for \( D E \):**
\[
D E = 61 - 18 = 43
\]
**Answer:** \( D E = 43 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve for \( DE \), we can utilize the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have the sides \( DF \) and \( EF \). Using the formula: \[ DE < DF + EF \quad \text{and} \quad DE > |DF - EF| \] Plugging in the values: \[ DE < 61 + 18 = 79 \] \[ DE > |61 - 18| = 43 \] Thus, the length of \( DE \) must be between \( 43 \) and \( 79 \). However, without additional information or constraints, we cannot determine an exact length.
