One side of the triangle is 5 centimeters larger than the other, and the angle between them is 60 degrees.

One side of the triangle is 5 centimeters larger than the other, and the angle between them is 60 degrees. Find the perimeter of the triangle if its third side is 7 cm.

1) let one side = x cm, then the other = (x + 5) cm
2) by the cosine theorem a ^ 2 = b ^ 2 + c ^ 2-2bc * cos (angle between b and c)
7 ^ 2 = x ^ 2 + (x + 5) ^ 2-2 * x * (x + 5) * cos60
49 = x ^ 2 + x ^ 2 + 10x + 25- (2x ^ 2 + 10x) • 1/2
49 = 2x ^ 2 + 10x + 25 + x ^ 2 + 5x
3x ^ 2 + 15x-24 = 0
x ^ 2 + 5x-8 = 0
D = 25 + 24 = 49
x1 = (- 5 + 7) / 2 = 1
x2 = (- 5-7) / 2 = -6 (does not satisfy the condition)
side 1 is 1 cm, side 2 is 1 + 5 = 6 cm
P = 1 + 6 + 7 = 14 cm
Answer: 14 cm