Points P and F, respectively, are the seridines of the edges BC and AB of the tetrahedron DABC.

Points P and F, respectively, are the seridines of the edges BC and AB of the tetrahedron DABC. Calculate the perimeter of the triangle DPF if the perimeter of the tetrahedron face is 36 cm.

The condition says that DABC is a tetrahedron (at the base is an equilateral triangle ABC, one of the vertices of D). We need to find the perimeter of the DPF, for this we will do this:

Let us calculate the side lengths of the base of the tetrahedron:

P = 3 * BC, therefore BC = P / 3 = 36 cm / 3 = 12 cm.

FP – is the midline of triangle ABC and to calculate its length we will use the formula:

FP = 12 cm / 2 = 6 cm.

Consider a triangle DCP, express the side PC from the formula for calculating the tangent:

tg 60 = DP / PC, therefore

PC = 6; DP = √3 * 6.

P of triangle DPF = 12√3 + 6.