To determine the length of QS in parallelogram PQSR, we need to recall how to calculate the perimeter of a parallelogram. The perimeter (P) of a parallelogram is calculated using the formula:
P = 2(a + b)
Where ‘a’ is the length of one side and ‘b’ is the length of the adjacent side. In this case, we know that the perimeter is 74 cm, so:
2(a + b) = 74
Dividing both sides by 2 gives us:
a + b = 37
Since we are interested in finding the length of QS, we need to consider that QS is one of the sides of the parallelogram. If we assume PQSR is structured such that PQ is equal to SR and PS is equal to QR, we can let:
QS = a and thus we also have QP = a.
To find QS, we would need additional information about the lengths of the sides. However, given that a + b = 37, if you know either ‘a’ or ‘b’, you can always find the other side. For example:
If you assume QS = 20 cm, then:
20 + b = 37
=> b = 17 cm.
So, without more information or constraints on the lengths of the sides, we can’t determine a unique value for QS. It could be any value less than 37 cm depending on the length of the other side. Hence, more information is needed to find the exact length of QS.