The perimeter of PNM if BC = 6 units, AB = 8 units, and NP = MP is B) Perimeter = 22 units.
We can find the perimeter of PNM by adding the lengths of its three sides.
Given that NP = MP, we assume that the triangle PNM is isosceles. Hence, the length of the side PN is equal to the length of the side PM.
Based on the Pythagorean theorem, the length of the side NM is as follows:
NM^2 = NP^2 + PM^2
NM^2 = 6^2 + 4^2
NM^2 = 36 + 16
NM^2 = 52
NM = sqrt(52)
NM = 2 * sqrt(13)
Therefore, the perimeter of PNM is:
PN + NM + PM
= 8 + 2 * sqrt(13) + 2 * sqrt(13)
= 8 + 4 * sqrt(13)
= 8 + 4 x 3.60555
= 22 units
Thus, the perimeter of PNM is 22 units.