Question #327549

A rectangular field is to be enclosed by a fence then subdivided into three areas by fences

parallel to the shorter side. Find the dimensions of the field with the largest total area that can be

enclosed with 260 m of fencing. What is the area?


1
Expert's answer
2022-04-12T15:55:54-0400

As rectangular field is divided into three areas the fence is consist of 4 short sides and 2 large sides.

Define xx m is a short side. Then (2604x)/2(260-4x)/2 m is a large side. Total area:

S(x)=x(2604x)/2S(x)=x(260-4x)/2

Let’s find x for which the total area is maximum:

S(x)=1304x=0S’(x)=130-4x=0

x=32.5x=32.5

As S(30)=130120>0S’(30)=130-120>0 and S(35)=130140<0S’(35)=130-140<0 we can conclude x=32.5x=32.5 corresponds to maximum value S(x)S(x).

Sides of the rectangular field:

32.5 m and (260432.5)/2=65(260-4\cdot32.5)/2=65 m.

Largest total area:

S=32.565=2112.5S=32.5\cdot65=2112.5 m2m^2


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS