2*(L+B) = 40

L+B = 20

LB = 64

Possible combination is 16 & 4

16 is present in answer choices

so [spoiler]{E}[/spoiler]

Let us solve this problem via back solving method.


Let's start with C, the middle value. If the length of the yard is 12 and the perimeter is 40, the width would be 8 (perimeter - 2l = 2w). With a length of 12 and a width of 8, the area would be 96. This is too big of an area.

It may not be intuitive whether we need the length to be longer or shorter, based on the above outcome. Consider the following geometric principle: for a fixed perimeter, the maximum area will be achieved when the values for the length and width are closest to one another. A (10 × 10) rectangle has a much bigger area than an 18 × 2 rectangle. Put differently, when dealing with a fixed perimeter, the greater the disparity between the length and the width, the smaller the area.

Since we need the area to be smaller than 96, it makes sense to choose a longer length so that the disparity between the length and width will be greater.

When we get to answer choice E, we see that a length of 16 gives us a width of 4 (perimeter - 2l = 2w). Now the area is in fact 16 × 4 = 64.

The correct answer is E