Answer:
the Largest shed dimension is 13.5 ft by 13.5 ft
Largest Area is 182.25 ft²
Step-by-step explanation:
Given that;
Perimeter = 54 ft
P = 2( L + B ) = 54ft
L + B = 54/2
L + B = 27 ft
B = 27 - L ------------Let this be equation 1
Area A = L × B
from equ 1, B = 27 - L
Area A = L × ( 27 - L)
A = 27L - L²
for Maxima or Minima
dA/dL = 0
27 - 2L = 0
27 = 2L
L = 13.5 ft
Now, d²A/dL² = -2 < 0
That is, area is maximum at L = 13.5 using second derivative test
B = 27 - L
we substitute vale of L
B = 27 - 13.5 = 13.5 ft
Therefore the Largest shed dimension = 13.5 ft by 13.5 ft
Largest Area = 13.5 × 13.5 = 182.25 ft²
