The sum of the lengths of the sides AB and BC of the triangle ABC = 11 cm. The sum of the lengths

| May 1, 2021 | education

The sum of the lengths of the sides AB and BC of the triangle ABC = 11 cm. The sum of the lengths of the sides BC and CA = 7 cm. And the sum of the lengths of the sides AB and CA = 8 cm. Nadi is the perimeter of triangle ABC. Find the length of each side?

1. Let’s compose expressions, according to the condition of the problem:
AB + BC = 11,
BC + CA = 7,
AB + CA = 8.
2.Now we add all the expressions together, we get:
2AB + 2BC + 2CA = 11 + 7 + 8,
2 * (AB + CA + BC) = 26,
AB + BC + CA = 26/2,
AB + CA + BC = 13 cm.
3. Since AB + BC + CA is the length of the perimeter of the triangle ABC, then the perimeter of the triangle is 13 cm.
4. Find each side of the triangle by subtracting from the perimeter a pair of sides given in the condition:
AB = 13 – 7 = 6 cm.
BC = 13 – 8 = 5 cm.
CA = 13 – 11 = 2 cm.
Answer: the perimeter of the triangle is 13 cm; AB = 6 cm, BC = 5 cm, CA = 2 cm.



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