In a polygon with perimeter 31, a diagonal B was drawn, which divided it into two polygons
| April 2, 2021 | education
In a polygon with perimeter 31, a diagonal B was drawn, which divided it into two polygons with perimeters 21 and 30. What is the length of B.
We represent the polygon in the form of a quadrilateral ABCD, since the result will be the same for any convex polygon.
Ravsd = 31 cm = AB + BC + СD + AD.
Pavd = 30 cm = AB + BD + AD. (one).
Рвсд = 21 cm = ВС + СD + ВD. (2).
Add equations 1 and 2.
30 + 21 = AB + BD + AD + BC + CD + BD.
51 = (AB + BC + CD + AD) + 2 * BD.
51 = 31 + 2 * BD.
2 * ВD = 51 – 31 = 20 cm.
ВD = 20/2 = 10 cm.
Answer: The length of the diagonal is 10 cm.
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