# The perimeter of the triangle is 27.8 cm. One side of the triangle is 3.5 cm larger than the other and 2.7 cm

**The perimeter of the triangle is 27.8 cm. One side of the triangle is 3.5 cm larger than the other and 2.7 cm larger than the third. Find what is the largest side.**

1. A, B, C – the vertices of a given triangle.

2. AB is more than BC by 3.5 centimeters. AB is larger than AC by 2.7 centimeters.

2. We take the length of the AB side as x (centimeters), the length of the BC side (x – 3.5) centimeters.

The length of the AC side = (x – 2.7) centimeters.

3. Considering that the total length of all sides of the triangle is 27.8 cm (the perimeter of the triangle), we compose the equation:

x + (x – 3.5) + (x – 2.7) = 27.8;

3x = 34;

x = 11 and 1/3 centimeters.

AB = 11 and 1/3 centimeters – the largest side of the triangle.

Answer: AB = 11 and 1/3 centimeters – the largest side of the triangle.