Can you do some of that calculus and tell me an L and W that multiply to 12 and a 2L+2W that add to one of the other choices? I’m just looking for one set of numbers and will concede.
At that point no calculus is needed, just algebra:
You want to solve L*W = 12 and 2L + 2W = P (for P any of the numbers, or for that matter any other number greater than 4 times the square root of 12 that you’d like for a perimeter and L, W positive, since they must represent lengths).
Thus L = P/2 - W, and we can substitute into the other equation get
(P/2 - W)*W = 12, which is equivalent to
0 = W^2 - (P/2)W + 12
Using the quadratic formula gives
W = [P/2 +/- sqrt ( (P/2)^2 - 4*1*12 )]/2*1
So as long as (1/4)P^2 >= 48 this has real solutions, which are easily seen to be positive.
So if you’d like P = 21, you get W = [21/2 +/- sqrt(441/4 - 48)]/2.
Pick the - for and W the + for L (If you go back to the equation we used to get rid of L and get an equation in W only you can see this is right.) Giving (approximately)
W = 1.30507 and L = 9.19493 (Ihe actual values are irrational numbers — it happens that the round-off errors in those approximations exactly cancel when computing the perimeter to give 21 on the nose, and multiplying gives 12 correct to six significant digits, just like the approximations I gave).
The problem would have been well-posed with the answer B if it had been specified that the blanket was rectangular with sides of lengths given by whole numbers of units, or even with sides of rational length.
(And it didn’t even say the blanket was rectangular. I’ve seen baby blankets with scalloped edges, or rounded-corners.)