To determine the length of QS in parallelogram PQSR, we first need to understand the properties of a parallelogram.
A parallelogram has opposite sides that are equal in length. This means that if we let the lengths of sides PQ and SR be equal to a, and the lengths of sides PS and QR be equal to b, the perimeter (P) can be expressed by the formula:
P = 2(a + b)
Given that the perimeter of parallelogram PQSR is 74 cm, we can write:
2(a + b) = 74
Dividing both sides of the equation by 2 gives us:
a + b = 37
Now, in a parallelogram, the diagonal QS can be derived using the law of cosines, but it requires knowing the angle between the sides. Without additional information about the angles or the lengths of the sides, we can’t compute the precise length of QS directly.
However, if we assume that PQ and PS are equal (i.e., the parallelogram is a rhombus), then we would have:
a = b
Thus, if both sides are equal, we find:
2a = 37 → a = 18.5 cm
In this special case, QS could be evaluated using the properties of a rhombus. But without more information, all we can conclude is that we need additional data to find a unique value for QS.
In summary, while we know the perimeter of the parallelogram is 74 cm, the length of diagonal QS depends on the specific dimensions of sides PQ and PS and the angles within the parallelogram.