Points D, E, F are the midpoints of sides ABC. The perimeter of triangle DEF is 5. Find the perimeter of triangle ABC.
| August 4, 2021 | education
1. A, B, C – the vertices of the triangle. DEF is a triangle formed by the middle lines. DE, EF, DF – middle lines.
2. The middle line of the triangle is equal to half of the side parallel to it. Therefore, AC = 2DE, AB = 2EF, BC = 2ДF.
3. The perimeter of the triangle DEF = DE + EF + DF = 5 centimeters.
4. The perimeter of the triangle ABC = AB + BC + AC.
5. We replace in the last expression AC with 2DE, AB with 2ЕF, BC with 2ДF.
The perimeter of the triangle ABC = 2DE + 2EF + 2DF. = 2 (DE + EF + DF) = 2 x 5 = 10 centimeters.
Answer: The perimeter of triangle ABC is 10 centimeters.
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