Question

Точки A,B,C и D не принадлежат одной плоскости. Точки K,L,M и N принадлежат соответственно отрезкам BD,AD, AC и BC так, что DK:KB= DM:MA= CL:LA= CN:NB=1:4, определите периметр четырехугольника KMLN, если AB=25, CD=30

Answer 1

Нужно просто немного подумать в принципе задание несложное я бы решила это так:
CN -NB =30-25=5
5*4:2=10
Все просто :3

Answer 2

Calculating the lengths of the sides

According to the information provided: - Points A, B, C, D do not lie in the same plane - Points K, L, M, N lie on segments BD, AD, AC, BC respectively - The ratios of the corresponding segments are: DK:KB = DM:MA = CL:LA = CN:NB = 1:4

DK = 4KB DM = 4MA CL = 4LA CN = 4NB

Using similar triangles

Triangle BKD is similar to triangle BKC. Therefore, the ratios of the corresponding sides are equal: DK/KB = BC/BK DK/KB = 4 (given) BC/BK = 4 BK = BC/4

Using the same approach for the other triangles, we get: MA = AC/4 LA = AB/4 NB = BC/4

Finding the perimeter

AB = 25 (given) CD = 30 (given) BC = AB/4 = 25/4 = 6.25

Perimeter of KMLN = DK + KM + ML + LN + CN = 4KB + 4MA + 4LA + 4NB + 4NB = BC + AC + AB + 2BC = 25 + 30 + 25 + 2×6.25 = 92.5