A farmer has 60m of fencing to make a rectangular pen for his goats.
Derive an expression in simplest form, for the length of the pen
To derive an expression for the length of the rectangular pen, let's first understand the problem.
We know that the farmer has 60 meters of fencing to make a rectangular pen for his goats. A rectangle has two pairs of equal sides, so let's assume that the length of the pen is L meters and the width is W meters.
Now, let's consider the perimeter of the rectangular pen. The perimeter of a rectangle is the sum of all its sides. In this case, we have two identical lengths (L + L) and two identical widths (W + W). Therefore, the perimeter can be calculated as:
Perimeter = 2L + 2W
But we also know that the farmer has 60 meters of fencing. So, the perimeter should be equal to 60:
2L + 2W = 60
To derive an expression for the length of the pen, let's isolate the length variable:
2L = 60 - 2W
Dividing both sides of the equation by 2, we get:
L = (60 - 2W) / 2
Simplifying the equation further, we have:
L = 30 - W
Therefore, the expression for the length of the rectangular pen in simplest form is L = 30 - W, where L represents the length and W represents the width of the pen.