# Rectangles ABCD and ABMC lie in different planes. The sum of their perimeters is 46 cm.

Rectangles ABCD and ABMC lie in different planes. The sum of their perimeters is 46 cm. AK = 6 cm, BC = 5 cm. Calculate the distance between the straight lines AK and BC.

Let’s construct rectangles ABCD in which BC = 5 cm and ABMK in which AK = 6 cm, they have a common side AB, it is perpendicular to the sides BC and AK – this means that this will be the distance between the straight lines BC and AK.
Perimeter of rectangle ABCD:
p1 = 2AB + 2BC.
The perimeter of the AВMK rectangle:
p2 = 2AB + 2MK.
Perimeter sum:
p = p1 + p2 = 2AB + 2BC + 2AB + 2MK = 4AB + 2BC + 2MK = 46.
Let’s substitute the numerical values:
4AB + 2 * 5 + 2 * 6 = 46.
Let’s solve the equation:
4AB = 46-10-12.
4AB = 24 cm.
AB = 6 cm.
Answer: the distance between the straight lines AK and BC is 6 cm.

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