SOLUTION: A farmer wants to divide his plot of land into 4 equal parts. He then will fence it in with 750 feet of fencing. Find a function that models the total area of the four pens.

Question 549019: A farmer wants to divide his plot of land into 4 equal parts. He then will fence it in with 750 feet of fencing. Find a function that models the total area of the four pens.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You can't do this problem exactly as it is stated. That is because there is no guarantee as to the shape of the plot of land.

Proceeding on the assumption that your problem should have read: "A farmer wants to divide his rectangular plot of land into 4 equal parts..."

Draw a rectangle. Construct a line segment with endpoints at the midpoints of the long sides of the rectangle. Construct a line segment with endpoints at the midpoints of the short sides of the rectangle. In sum, you will have 6 line segments that each measure one-half of the length of your rectangle and an additional 6 line segments that each measure one-half of the width of the rectangle. Therefore the total measure of the the line segments is

, and we are given that this total measure must be 750 feet, so:

which is to say

Since the area of the original rectangle is given by

, then your Area (as a function of the width of the rectangle) would be:

Of course, all bets are off if the original plot was in the shape of a parallelogram, trapezoid, or some other odd-ball quadrilateral, or an ellipse, or...?

The area of a square field so divided and fenced would be exactly:

square feet.

Which, by the way, is the maximum possible area for any rectangular shaped field.

The area of a circular field so divided and fenced would be exactly:

Which is approximately

square feet

and any other regular polygon (except an equilateral triangle) would have an area somewhere between those limits.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

RELATED QUESTIONS
Farmer Fred had a square field with sides of 525 feet. He wants to build a fence down one (answered by ad_alta)

This is a quadratic word problem. A farmer wishes to enclose a rectangular region... (answered by ankor@dixie-net.com)

a farmer needs to enclose a rectangular field with a fence down the middle to divide it... (answered by ikleyn,Edwin McCravy)

A farmer wants in enclose a rectangular plot of land with an area of 600 sq.ft. that... (answered by ankor@dixie-net.com)

A farmer has 120m of fencing. He wants to put a fence around three sides of a rectangular (answered by greenestamps,ikleyn)

Max/Min Applications. A farmer with 10,000 feet of fencing wants to enclose a... (answered by solver91311)

Hey guys im having a hard time with this word problem. Ive spent about 2 hours trying to... (answered by Theo)

a rectangular plot of land has a perimeter of 4,800 ft. A farmer wants to build a fence... (answered by checkley79)

a farmer with 1000 feet of fencing wants to enclose a rectangular field. Within this... (answered by math_helper)