Question

A carpenter is building a rectangular shed with a fixed perimeter of 54 ft. What are the dimensions of the largest shed that can be built? What is its area?

Answer 1

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