The AB side of the ABC triangle is 7cm larger than the AC side, which is 6cm less from the BC side. find the sides of a triangle whose perimeter is 49cm
According to the terms of the assignment, firstly, the AB side of the ABC triangle is 7 cm larger than the AC side, that is, AB = AC + 7 cm.Secondly, the AC side is 6 cm less from the BC side, that is, AC = BC – 6 cm Let us substitute this expression for AC into the equality of the first condition: AB = BC – 6 cm + 7 cm = BC + 1 cm.
Thirdly, the perimeter of the triangle is 49 cm, that is, AB + AC + BC = 49 cm. Let’s substitute the found expressions for AB and AC into this equality. Then, we get: BC + 1 cm + BC – 6 cm + BC = 49 cm or 3 * BC = 49 cm – 1 cm + 6 cm = 54 cm, whence BC = (54 cm): 3 = 18 cm.
Let’s calculate the other sides: AB = 18 cm + 1 cm = 19 cm and AC = 18 cm – 6 cm = 12 cm.
Note that a triangle with sides AB = 19 cm, AC = 12 cm and BC = 18 cm satisfies the conditions for the existence of a triangle.
Answer: AB = 19 cm, AC = 12 cm and BC = 18 cm.
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