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If \( A D=13 \) units and \( D C=5 \) unis, calculate the length of ED.

Ask by Mckenzie Lambert. in South Africa
Mar 11,2025

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Tutor-Verified Answer

Answer

\( ED = \frac{\sqrt{194}}{2} \) units.

Solution

1. Since the problem involves points \( A \), \( D \), and \( C \) with given lengths \( AD=13 \) and \( DC=5 \), we assume that \( \angle ADC \) is a right angle. In a right triangle, the midpoint of the hypotenuse is the circumcenter. Thus, if we let \( E \) be the midpoint of \( AC \), then \[ ED = \frac{AC}{2}. \] 2. Compute the length of the hypotenuse \( AC \) using the Pythagorean theorem: \[ AC = \sqrt{AD^2 + DC^2} = \sqrt{13^2 + 5^2} = \sqrt{169 + 25} = \sqrt{194}. \] 3. Therefore, the length of \( ED \) is: \[ ED = \frac{\sqrt{194}}{2}. \]

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To calculate the length of \( ED \), we need to determine the relationship between the points \( A, D, C, \) and \( E \). However, based on the information provided (i.e., \( AD = 13 \) units and \( DC = 5 \) units), it's unclear how \( E \) is connected to these points. Assuming \( E \) lies on the line segment \( AC \), we can first find the length of \( AC \) by adding \( AD \) and \( DC \): \[ AC = AD + DC = 13 + 5 = 18 \text{ units.} \] Without additional context regarding point \( E \)'s position along \( AC \) or any other geometric properties, we cannot definitively calculate the length of \( ED \). If \( E \) was meant to be at any specific location relative to \( D \) or the segment \( AC \), further details are needed to solve for \( ED \). Could you provide more information about where \( E \) is located?

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