In the MIC triangle, point F is the midpoint of the MI side. It is known that the perimeter of triangle

In the MIC triangle, point F is the midpoint of the MI side. It is known that the perimeter of triangle F MK is 26 cm less than the perimeter of triangle IKF. Find MK if IR = 51 cm.

Since F is the middle of the MI side, it follows that MF = FI.

The perimeter of the triangle FMK is (MF + MK + KF).

The perimeter of the triangle IKF is (IK + FI + KF).

By condition, the difference between their perimeters is 26 centimeters.

Then we compose and solve the equation

MF + MK + KF + 26 = IК + FI + KF;

MK + 26 = IК;

MK = IК – 26;

MK = 51 – 26 ;;

MK = 25.

Answer: the length of the MK side is 25 centimeters.