The perimeter of the triangle ABC is 46 5/8 cm. The sum of the sides AB and BC is 31 1/4 cm, and the sum
| July 5, 2021 | education
The perimeter of the triangle ABC is 46 5/8 cm. The sum of the sides AB and BC is 31 1/4 cm, and the sum of the sides AB and AC is 28 5/16 cm. Find the sides of the triangle.
The perimeter of the ABP triangle is:
Ravs = AB + BC + AC = 46 (5/8) = 373/8.
By condition, AB + BC = 31 (1/4) = 125/4.
Substitute this value into the perimeter equation.
125/4 + AC = 373/8.
AC = 373/8 – 125/4 = 373/8 – 250/8 = 123/8 = 15 (3/8).
AB + AC = 28 (5/16) = 453/16.
AB = 453/16 – AC = 453/16 – 123/8 = 453/16 – 246/16 = 207/16 = 12 (1516).
Then BC = Ravs – AC – AB = 373/8 – 123/8 – 207/16 = 746/16 – 246/16 – 207/16 = 293/16 = 18 (5/16).
Answer: The sides of the triangle are equal: AC = 15 (3/8), AB = 12 (15/16), BC = 18 (5/16).
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