Maria’s garden has 24 meters of fence and she wants to fence the rectangular garden with wall on one side of the garden. She needs no fence along the wall side. Find the largest area of the Maria’s farm that can be fenced.

Answer 1

24/3 = 8

8 * 8 = 64 square meters

Answer 2

let the length parallel to the wall by y m
let the other two lengths be x m
2x + y = 24
y = 24-2x

area = xy
= x(24-2x)
= -2x^2 + 24x

this is a downwards opening parabola, we have to find the vertex.
I don't know which method you use but the easiest way is to find the x of the vertex with -b/(2a)
= -24/(4)
= 6
when x=6 , y = 24-12 = 12
The long side has to be 12 m and each of the shorter sides 8 m


the maximum area is 6(12) = 72 m^2

Note , the sum of the 3 sides is 24