Question

Find the largest area which the farmer can enclose with 56m of fencing materials.

28-x
x ⬜ x
28-x​

Answer 1

Answer:

219.4545..

Step-by-step explanation:

The largest area can be covered by a circle.

so 2$\pi$r = 56

        r = 98/11

Therefore area covered by the circle would be

$\pi$$r^{2}$ = 22/7 * $(98/11)^{2}$  = 219.45454

But if it is to be a rectangular / square field

The largest area would be:

1. For a square field:

   Perimeter = 56 , therefore one side = 14 and therefore area = 14^2 = 196

2. For a rectangular field:

   Perimeter = 56

   2(a+b) = 56

    a+b = 28

    a = 28 - b

   Therefore area would be >196 (ie, smaller than area of the square field) as there is going to be a difference of squares.