Answer:
1. The pattern that I observe in the table above is that the fixed perimeter of these rectangles are 24 meters, and that the graph to represent this function is in the shape of a parabola with a vertex point at (6, 36). As for comparing the patterns to the graph in question A, assuming you're referring to the question I just answered, the graphs both are parabola shaped, with a vertex point and two zeros, one of them being the same at the origin of the coordinate plane (0, 0).
2. The fixed perimeter for the rectangles represented by this table is 24 meters because if you want to find the fixed perimeter of these rectangles, you can pick any point that is not a zero point of the graph. For example, if the length of a rectangle is 1 meter, and the area is 11
, we know the width would be 11 meters. Using this information, we know that the fixed perimeter would be (1 + 11) × 2 = 12 × 2 = 24 meters.
3. The greatest area possible for a rectangle with a perimeter of 24 meters would be 36
because we can graph these points to form a parabola that represents this situation, and the vertex point of this graph would be the greatest area possible out of all the possible combinations of length and width that would still fit the criteria of having a perimeter of 24 meters.
Based on the table, the vertex point of the graph would be (6, 36), therefore the greatest area possible for a rectangle with this perimeter would be 36
. As for the dimensions of this rectangle, we know the length is 6 meters, and the area is 36
, so the width would be 36 ÷ 6 = 6 meters. Therefore the dimensions of this rectangle would be 6 meters in length and 6 meters in width.
Have a great day! Feel free to let me know if you have any more questions :)