Points C, H, P are the midpoints of the sides of triangle ABK. Find the perimeter of triangle CHP

| February 13, 2021 | education

Points C, H, P are the midpoints of the sides of triangle ABK. Find the perimeter of triangle CHP if the sides of triangle ABK are 12, respectively; 9; 8.

First way.

Since points C, H, P are the midpoints of the sides of the triangle ABK, then the segments CH, CP, HP are the midlines of the triangle ABK.

Then CH = AK / 2 = 12/2 = 6 cm, СР = ВK / 2 = 9/2 = 4.5 cm, HP = AB / 2 = 8/2 = 4 cm.

Then the perimeter of the CHP triangle is equal to: Pcnr = (CH + CP + HP) = (6 + 4.5 + 4) = 14.5 cm.

Second way.

Since points C, H, P are the midpoints of the sides of triangle ABK, the triangles ABK and CHP are similar in three proportional sides. With a coefficient of similarity 1/2.

Then Rsnr = Ravk / 2 = (12 + 8 + 9) / 2 = 14.5 cm.

Answer: The perimeter of the CHP triangle is 14.5 cm.



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