Question

While forming different rectangles by arranging $16$ unit square crackers, which of the following arrangement will have the maximum perimeter?

• A. $16\times 1$
• B. $8\times 2$
• C. $4\times 4$
• D. All of them will have equal perimeters.

Answer 1

The correct option is A $16\times 1$

Rearranging $16$ unit square crackers, we get the following three combinations:
Figure 1. $16\times 1$
For this arrangement, its perimeter
$=2\times (16+1)=34$ units.

Figure 2. $2\times 8$
For this arrangement, its perimeter
$=2\times (8+2)=20$ units.

Figure 3. $4\times 4$
For this arrangement, its perimeter
$=2\times (4+4)=16$ units.
$\therefore 1\times 8$ arrangement will have the maximum perimeter.