The perimeter of the triangle is 102 cm. One side is 8 cm shorter than the other and its length is 2 cm

The perimeter of the triangle is 102 cm. One side is 8 cm shorter than the other and its length is 2 cm longer than the doubled length of the third side. Find the lengths of the sides of the triangle.

Let the third side of the triangle be x cm, then the second will be equal to (2 + 2x) cm, and the first – (2 + 2x – 8) cm. Knowing the value of the perimeter of a triangle with such sides and that the perimeter is the sum of all sides, we can make equation and solve it:

2 + 2x – 8 + 2 + 2x + x = 102;

5x = 102 – 2 + 8 – 2;

5x = 106;

x = 106/5;

x = 21.2.

If x = 21.2, then the third side is 21.2 cm, the second is 44.4 cm, and the first is 36.4 cm.

Answer: 36.4 cm, 44.4 cm, 21.2 cm.

Verification:

36.4 + 44.4 + 21.2 = 102;

102 = 102.