Answer:
(i) The area of the rabbit cage when the width is 5.2 m is 81.5 m²
(ii) The area of the rabbit cage if Wilson has 40 meters of wire mesh is 75 m²
Explanation:
(i) The given relation of the area, A to the width P of the rabbit cage is A = 3·p²
The graph of the function between the values of 0 and 6 inclusive is found as follows;
A, 3·p²
0, 0
1, 1
2, 12
3, 27
4, 48
5, 75
6, 108
Please find attached the graph of A to 3·p²
From the graph, we have when the the width, p, of the rabbit cage = 5.2, the area, A ≈ 81.5 m²
The area of the rabbit cage when the width is 5.2 m = 81.5 m²
(ii) Also from the graph given that the total wire mess with Wilson = 40 meters, we have;
The formula for the perimeter of the cage = The formula for the perimeter of a rectangle = 2×length + 2×width
The formula for the perimeter of the cage = 2×3×p + 2× p = 8·p
Where the total length of the wire mesh available = 40 meters for the cage
The 40 meters of wire mesh will be used round the perimeter of the cage
∴ 40 m. = 8·p
p = 40/8 = 5 m.
At p = 5 m. the area is given as A = 75 m².
Therefore, the area of the rabbit cage if Wilson has 40 meters of wire mesh = 75 m².