Make an expression to solve the problem and find its value: In triangle ABC, the length of side AB is 5 cm

| March 17, 2021 | education

Make an expression to solve the problem and find its value: In triangle ABC, the length of side AB is 5 cm, side BC is 8 cm longer than side AB, and the length of side AC is less than the sum of the lengths of sides AB and BC by 6 cm. Find the perimeter of the triangle.

The solution of the problem.
1) The perimeter of a triangle is equal to the sum of the lengths of all its sides, that is, it can be written that P = AB + BC + AC.
2) BC = AB + 8.
3) AC = AB + BC – 6 = AB + (AB + 8) – 6 = AB + AB + 8 – 6 = 2AB + 2.
4) Then the expressions for the perimeter of the triangle can be written as follows:
P = AB + BC + AC = AB + (AB + 8) + (2AB + 2) = AB + AB + 8 + 2AB + 2 = 4AB +10.
5) Find the perimeter of the triangle, knowing that the length of the side AB is 5 cm:
P = 4 * 5 + 10 = 20 + 10 = 30 cm.
Answer: P = 4AB + 10; P = 30 cm.



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