The perimeter of triangle mpk is 34 cm. Point P lies on the MK side of this triangle so that the sum

The perimeter of triangle mpk is 34 cm. Point P lies on the MK side of this triangle so that the sum of the perimeters of triangle MPH and triangle KPH is 60 cm. Find the length of the segment PH.

By condition, PMPK = MP + PK + MK = 34 cm.

PMPH = MP + PH + MH;

PKPH = KP + PH + KH.

PMPH + PKPH = 60;

MP + PH + MH + KP + PH + KH = 60.

Since point H lies on the side of MK, it means MH + KН = MK. Means:

MP + PH + MH + KP + PH + KH = MP + PK + MK + 2 * PH = PMPK + 2 * PH = 60;

34 + 2 * PH = 60;

2 * РН = 60 – 34 = 26;

PH = 26/2 = 13 cm.