Final answer:
To find the perimeter of quadrilateral B, the scale factor is calculated using the ratio of the longest sides, which is 3.5. Multiplying each side length of quadrilateral A by this scale factor produces the side lengths of quadrilateral B. Summing these gives a perimeter of 56, which is not among the given options.
Step-by-step explanation:
The student's question involves finding the perimeter of a quadrilateral B that is a scaled copy of quadrilateral A. The side lengths of quadrilateral A are 2, 3, 5, and 6, and the longest side of quadrilateral B is 21. To calculate the perimeter of quadrilateral B, we need to determine the scale factor between the two quadrilaterals.
Since the longest side of quadrilateral A is 6, and the corresponding longest side of quadrilateral B is 21, the scale factor is determined by the ratio 21/6, which simplifies to 3.5. Therefore, all side lengths of quadrilateral A must be multiplied by 3.5 to obtain the side lengths of quadrilateral B. Calculating these, we get 2 * 3.5 = 7, 3 * 3.5 = 10.5, 5 * 3.5 = 17.5 and 6 * 3.5 = 21.
Finally, the perimeter of quadrilateral B is the sum of its side lengths: 7 + 10.5 + 17.5 + 21 = 56. This is not one of the options provided in the question, indicating that there might be an error in the question options or in the interpretation of the problem. The correct answer is not listed among options (a) through (d).