Find the two sides of the triangle if their difference is 28 cm and the sectoral line drawn

Find the two sides of the triangle if their difference is 28 cm and the sectoral line drawn to the third side divides it into segments 43 cm and 29 cm.

Let one of the sides of the triangle be equal to x, then the second is equal to x + 28.

It is known that the bisector of a triangle divides the side to which it is drawn into segments, the ratio of which is equal to the ratio of the other two sides. Hence:

43/29 = (x + 28) / x;

43 * x = 29 * (x + 28);

43 * x = 29 * x + 812;

43 * x – 29 * x = 812;

14 * x = 812;

x = 812/14 = 58.

One of the required sides of the triangle is 58 cm, the second is 58 + 28 = 86 cm.