Question

The owner of a motel has 2900 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway. If she does not fence the side along the highway, what is the largest area that can be enclosed?

Answer 1

Answer:

Step-by-step explanation:

Given that the owner of a motel has 2900 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway.

Fencing is used for 2times length and 1 width if highway side is taken as width

So we have 2l+w = 2900

Or w = 2900-2l

Area of the rectangular region = lw

$A(l) = l(2900-2l) = 2900l-2l^2$

Use derivative test to find the maximum

$A'(l) = 2900-4l\\A"(l) = -4$

So maximum when I derivative =0

i.e when $l =\frac{2900}{4} =725$

Largest area = A(725)

= $725(2900-2*725)\\= 1051250$

1051250 sqm is area maximum