Final answer:
The perimeter of rectangle LMNP is found by adding twice the length of one vertical side (LP or MN) and twice the length of one horizontal side (LM or NP), which results in a total perimeter of 82 units.
Step-by-step explanation:
To calculate the perimeter of the rectangle LMNP with given vertices L(4,6), M(36,5), N(36,15), and P(4,15), we can use the distance formula or simply observe the coordinates to find the lengths of the sides. Since points L and P have the same x-coordinate, their distance apart is the difference in y-coordinates. The same logic applies to points M and N. Then we double those two distances to account for both pairs of opposite sides in the rectangle.
Length LP or MN (vertical sides) = |15 - 6| = 9 units
Length LM or NP (horizontal sides) = |36 - 4| = 32 units
Using the perimeter formula P = 2l + 2w:
P = 2(9) + 2(32) = 18 + 64 = 82 units
Therefore, the correct answer is A. 82 units.