b The formula for the area that is enclosed by the fencing a

b. The formula for the area that is enclosed by the fencing and the river is A=lw.

Solve the equation in part a.a. for ll, and then use the result to write the area in terms of ww only.
A(w)=________________________

  
c. What is the largest area that can be enclosed by the 400 yards of fencing?

The largest area that can be enclosed by the 400 yards of fencing is _____________ square yards.

Width (w) Length (l) River

Solution

Given that a total of 400 yards of fencing is to be used to enclose part of a lot that borders on a river.

a) An equation that gives the relationship between the length and width and the 400 yards of fencing:

This is nothing but the perimeter.

Perimeter = l + w + w = 400yards

l + 2w = 400yd

Therefore, required equation is  l + 2w = 400yd

b)Given Area A = lw

Need to write Area interms of w only.

From perimeter equation, l + 2w = 400yd

      l = 400 - 2w

A = lw

A(w) = (400 - 2w) * w

= 400w - 2w².

Therefore, area in terms of w only is A(w) = 400w - 2w².

c) Need to find largest area enclosed by the 400 yards of fencing.

For large area first derivative of A(w) with respect to w is zero.

A(w) = 400w - 2w².

A\'(w) = 400 - 2(2w).

0 =  400 - 4w.

400 = 4w

100 = w

So, w= 100yd.

l = 400-2w = 400 - 2(100) = 400-200 = 200

l = 200yd

Area = lw

= 200*100

= 20,000 square yards.

Therefore, largest area that can be enclosed by the 400 yards of fencing is 20,000square yards.