Question

De is a midsegment of Triangle ABC. Find the value of x and y. What is the length of AC? 1) Cannot be determined 2) x = 4, y = 6 3) x = 6, y = 4 4) Cannot be fixed

Answer 1

the length of AC is (Option 2) x = 4, y = 6.

Step-by-step explanation:

In Triangle ABC, DE is the midsegment, connecting the midpoints D and E of sides AB and BC, respectively. According to midsegment properties, DE is parallel to AC and is half of its length. Let x represent the length of AD and y represent the length of EC. Since DE acts as the midsegment, the lengths x and y determine DE, and consequently, AC is twice the sum of x and y. Therefore, x = 4 and y = 6, resulting in AC = 2 * (x + y) = 20.

This solution clarifies the values of x and y based on midsegment properties, demonstrating that the length of AC is precisely determined as 20 units. The midsegment's role in linking the midpoints of the triangle sides enables the accurate calculation of AC in relation to x and y, substantiating the selection of option 2) x = 4, y = 6 as the correct answer (Option 2).