Answer:
A = (100 - y)y
Maximum area = 2500 sq. feet.
Step-by-step explanation:
Let the length of the combined rectangular area is y feet and the shared width is x feet.
So, perimeter of the two rectangle together is (3x + 2y) = 200 {Given}
⇒ 2y = 200 - 3x
⇒ [tex]y= \frac{1}{2} (200 - 3x)[/tex] ...... (1).
a) Now, area of the total plot in sq. feet is [tex]A = xy = \frac{1}{2} (200 - 3x)x[/tex] ........ (2)
So, this is the expression for area A in terms of length of shared side x.
b) For area to be maximum the condition is [tex]\frac{dA}{dx} = 0[/tex]
Now, differentiating equation (2) on both sides with respect to x we get
[tex]\frac{dA}{dx} = 100 - 3x = 0[/tex]
⇒ x = 33.33 feet.
So, from equation (1) we get [tex]y= \frac{1}{2} (200 - 3x)[/tex]
⇒ x = 50 feet.
So, the value of maximum area = 50 × 33.33 = 1666.5 sq. feet. (Answer)
