1) A rancher wants to enclose two rectangular areas near a river, one for sheep and one for cattle. There is 240m of fencing available. Express the area of the enclosures as a function of its dimension.
No there is no common side (lets say.)
Thanks
To express the area of the enclosures as a function of its dimensions, we need to determine the dimensions of the rectangles. Let's assume the sheep enclosure has a length of L1 and a width of W1, and the cattle enclosure has a length of L2 and a width of W2.
The perimeter of the sheep enclosure can be calculated as follows:
Perimeter1 = 2L1 + 2W1
The perimeter of the cattle enclosure can be calculated as follows:
Perimeter2 = 2L2 + 2W2
Given that there is 240m of fencing available, we can write an equation using the perimeters of the two enclosures, as follows:
Perimeter1 + Perimeter2 = 240
Substituting the expressions for Perimeter1 and Perimeter2, we have:
2L1 + 2W1 + 2L2 + 2W2 = 240
Now, we can express the area of each enclosure in terms of its dimensions:
Area1 = L1 * W1
Area2 = L2 * W2
To solve this problem fully, we need additional information. Specifically, we need to know if there are any constraints on the dimensions or any relationships between the dimensions of the two enclosures. Without these constraints, we cannot express the area as a single function of its dimensions.