In a regular triangular pyramid with a base side 40 and a side edge 25 through a point dividing the side edge in a ratio of 2: 3

| February 7, 2021 | education

In a regular triangular pyramid with a base side 40 and a side edge 25 through a point dividing the side edge in a ratio of 2: 3 (from the top of the pyramid), a plane is drawn parallel to the opposite edge. Find the perimeter of the section

The section is an isosceles triangle MCR in which the sides KR and KM are parallel to the edges DВ and DС.

Let us calculate the lengths of the segments AK and DC. By condition, DC / AK = 2/3.

DC = 2 * AK / 3.

DA = DC + AK = 5 * AK / 3 = 25 cm.

AK = 15 cm.

Triangles DAВ and AKP are similar in two angles, then DВ / KР = AD / AK.

KР = DВ * AK / AD = 25 * 15/25 = 15 cm, then KM = 15 cm.

Determine the length of the segment AP.

AD / AВ = AK / AР.

AR = AB * AK / AD = 40 * 15/25 = 24 cm.

Triangles ABC and AMP are similar in two angles. Then BC / MP = AB / AP.

MР = BC * AР / AB = 40 * 24/40 = 24 cm.

Then Psech = KM + KР + MР = 15 + 15 + 24 = 54 cm.

Answer: The perimeter of the section is 54 cm.



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