Answer:
yes it is possible
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