Final answer:
To calculate the perimeter of parallelogram ABCD, we use the distance formula to determine one side and then double it for the pair of parallel sides. The given diagonal length splits into two equal lengths for the other pair of parallel sides. The calculated perimeter is approximately 16.4 units, but rounding discrepancies may lead to the closest option being 17.0 units.
Step-by-step explanation:
To find the approximate perimeter of parallelogram ABCD, we need to calculate the lengths of all sides. Since A(0,0) and B(3,3) form one side of the parallelogram, we can use the distance formula to calculate this side's length, which will then be the same for the opposite side due to the properties of a parallelogram. The distance formula is √((x2-x1)² + (y2-y1)²), which gives us √((3-0)² + (3-0)²) or √(9+9), which equals to √18 or approximately 4.2 units.
The length of the diagonal BD is given as 8 units. Since the diagonals of a parallelogram bisect each other, the length of the sides adjacent to point A (and similarly opposite to point A) are equal to half the diagonal, thus they are 4 units each. Therefore, adding up the lengths of all four sides, we get 4.2 units + 4.2 units + 4 units + 4 units, which equals 16.4 units. When we round each calculation to the tenths place, we get an approximate perimeter of 16.4 units.
Based on the given options, none of them exactly match our calculation. However, the closest option would be 17.0 units, which suggests a possible rounding or calculation difference in the method used to derive the options provided in the question or a misinterpretation of the information given.