Area of a Impossible rectangle

length/breath = 31 meter

breath/length = 1 meter

perimeter = 31 + 31 + 1 + 1 = 64 meters

$\begin{aligned} h \times b &= 31 \\ h \times b &= 31 \times 1 &\blue{\text{Only Possible product pair}} \end{aligned}$

W.L.O.G. let $h = 31, b = 1$ . Then we get perimeter as $2 (31 + 1) = \boxed{64}$

$\mathbf{Known \: \: Information:}$ $\\$ $\cdot$ $31$ is a prime number $\\$ $\cdot$ The area of a rectangle is equal to its $length \times width$ $\\$ $\cdot$ Perimeter is calculated by adding all side lengths of a shape $\\$

$\mathbf{Solving:}$ $\\$ A prime number only has two factors ( $1$ and itself), meaning that the edge lengths of the rectangle would be $31$ and $1$ . The perimeter of the rectangle would be $2$ ( $31$ ) $+$ $2$ ( $1$ ) $=$ $\boxed{{\color{#20A900}64m}}$

Since 31 is a prime number, it can be only expressed in the form of 31 x 1. So, the length and breadth of the rectangle is 31 and 1 respectively. Substituting the values in the formula. We get, Perimeter = 2( l + b ) = 2( 31 + 1 ) = 2(32) =64