# Points D and E are marked in triangle ABC, which are the midpoints of sides AB and BC, respectively.

January 15, 2021 | education

| **Points D and E are marked in triangle ABC, which are the midpoints of sides AB and BC, respectively. Find the perimeter of the quadrangle ADEC if AB = 24 cm, BC = 32 cm, AC = 44 cm**

1. The segment DE is the middle line of the triangle ABC, since it connects the midpoints of its two sides AB and BC.

2. The middle line DE of the triangle ABC is equal to half of the side of the AC:

DE = AC / 2 = 44: 2 = 22 cm.

3. Since point D is the midpoint of side AB, the length of the ABP segment is 24: 2 = 12 cm.

4. Since point E is the middle of the side BC, the length of the segment CE is 32: 2 = 16 cm.

5. The perimeter of the ADEC quadrilateral is 44 + 22 + 12 + 16 = 94 cm.

Answer: the perimeter of the ADEC quadrangle is 94 cm.

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