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

| May 26, 2021 | education

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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