Final answer:
The shortest side of the quadrilateral, whose sides are four consecutive odd numbers and the perimeter is 96, is 21 units.
Step-by-step explanation:
The student's question pertains to finding the lengths of the sides of a quadrilateral, given that they are four consecutive odd numbers and the perimeter sums to 96. To solve this, we first consider what consecutive odd numbers are like. If we let the smallest of these consecutive odd numbers be represented as n, the next three odd numbers would be n+2, n+4, and n+6, respectively.
Since the perimeter of a quadrilateral is the sum of all its sides, we can write the equation for the perimeter as:
n + (n+2) + (n+4) + (n+6) = 96
Simplifying this equation, we get:
4n + 12 = 96
Subtracting 12 from both sides gives us 4n = 84. Dividing both sides by 4 yields n = 21. Therefore, the length of the shortest side is 21 units.