# The first side of the triangle is 15 cm larger than the second, and the third is 1, 4 times less than the sum

**The first side of the triangle is 15 cm larger than the second, and the third is 1, 4 times less than the sum of the lengths of the first two sides. Find the lengths of all sides of a triangle if its P = 120 cm?**

Let x cm be the first side of the triangle, then (x + 15) cm is the second side of the triangle, and the third is ((x + x + 15): 1.4) = (2 * x + 15): 1.4 cm. By the condition of the problem, it is known that the perimeter of the triangle is 120 cm.

Let’s make the equation:

x + x + 15 + (2 * x + 15): 1, 4 = 120,

2 * x + 15 + (2 * x + 15): 1, 4 = 120, multiply both sides of the equation by 1.4:

2.8 * x + 21 + 2 * x + 15 = 168,

2.8 * x + 2 * x = 168 – 21 – 15,

4.8 * x = 132,

x = 132: 4.8,

x = 27.5 cm – the first side of the triangle.

2) 27.5 + 15 = 42.5 (cm) – the second side.

3) (27.5 + 42.5): 1.4 = 50 (cm) – third side.

Answer: 27.5 cm, 42.5 cm and 50 cm.