The perimeter of triangle ABC is 17.82 cm. Side BC is 1.3 times longer than side AB, and side AC

The perimeter of triangle ABC is 17.82 cm. Side BC is 1.3 times longer than side AB, and side AC is 1.75 times longer than side AB. Find the lengths of the sides of the triangle ABC.

Let the third side of triangle AB be x cm, then the second BC will be equal to 1.3x cm, and the first AC – 1.75x cm.Knowing the value of the perimeter of triangle ABC with such sides and that the perimeter is the sum of all sides, we can write an equation and solve it:

x + 1.3x + 1.75x = 17.82;

4.05x = 17.82;

x = 17.82 / 4.05;

x = 4.4.

If x = 4.4, then the third side AB will be 4.4 cm, the second BC will be 5.72 cm, and the first AC will be 7.7 cm.

Answer: 7.7 cm, 5.72 cm, 4.4 cm.

Examination:

7.7 + 5.72 + 4.4 = 17.82;

17.82 = 17.82.