Answer:
12m²
Step-by-step explanation:
For a rectangle, with length L and width W,
the perimeter is given as
Perimeter,
P = (2 x Length) + (2 x Width)
P = 2L + 2W
It is given that the perimeter is 48, hence
48 = 2L + 2W (divide both sides by 2)
24 = L + W
or
L = 24 - W -----> eq 1
Also realize that the Area of a Rectangle is given by
A = L x W -----> eq 2
Substituting eq 1 into eq 2,
A = (24 - W) x W
A = -W² + 24W
Recall that for a quadratic equation y = ax² + bx + c, the maxima or minima is given by y(max) = -b/2a
In this case, b = 24 and a = -1
-b/2a = -24/[ 2(-1) ] = 12
Hence for A to be maximum A(max) = 12m² (Answer)
