Final answer:
To find the length of side QS in parallelogram PQSR, subtract the length of side PQ from 37 cm.
Step-by-step explanation:
To find the perimeter of parallelogram PQSR, we need to add up the lengths of all four sides. Let's call the length of side PQ 'x' and the length of side QR 'y'. Since opposite sides of a parallelogram are equal in length, we know that the length of side SR is also 'x' and the length of side PS is 'y'. The perimeter of the parallelogram is then given by the equation:
P = PQ + QR + SR + PS
P = x + y + x + y
P = 2x + 2y = 74
From this equation, we can solve for the values of 'x' and 'y' by dividing both sides by 2:
x + y = 37
Since we are asked to find the length of side QS, which is equal to 'y', we can substitute 'y' with 37 - 'x' in the equation:
37 - 'x' = QS
Since the choices given are in centimeters, let's convert our equation to centimeters:
37 cm - 'x' cm = QS cm
Therefore, the correct answer is QS = 37 cm - 'x' cm.