a farmer has 96 meters of fencing with which to build a rectangular shaped pen for his pigs. Determine if it is possible for the pen to have a total area of 540 square meters

yes it is possible

Step-by-step explanation:

for the rectangular pen, let the width be W and the Length be L,

hence the area of the pen would be:

Area = W x L

We are given that the area is to be 540. Substitute this into the equation:

WL = 540   (in order to make the next step easier, we will express W in terms of L by dividing both sides by L)

W = 540 / L (eq 1)

Similarly, the perimeter of the rectangular pen would be

Perimeter = L + L + W + W

Perimeter = 2L + 2W (substitute the given perimeter = 96 meters)

96 = 2L + 2W   (divide both sides by 2)

L + W = 96/2

L + W = 48   (as in equation 1, we will express W in terms of L by subtracting L from each side)

W = 48 - L (eq 2)

if we equate (eq1) = (eq2)

540/L = 48 - L  (multiply both sides by L)

540 = L (48 - L)

540 = 48L - L²  (rearranging)

L²- 48L + 540 = 0    (solving by factorization)

(L-18)(L-30) = 0

Hence L = 18 meters or L = 30 meters

Now we find the corresponding values for W by substituting our values for L into equation 2

For L = 18 , W = 48 - 18 =30  (Hence L = 18 and W = 30 is one possible combination)

For L = 30, W = 48 - 20 = 18  (we can in L = 30 and W = 18 is another possible combination)

Since we can real solutions for L and W, we can conclude that it is possible to have an area of 540 m² and a perimeter of 96m

expression #3 is not equivalent. the others are.