Area Word Problem + Graph Problem

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SUMMARY

The discussion focuses on solving a goat rancher's fencing problem, specifically Problem #24, which requires constructing an equation to determine the maximum area that can be enclosed with 1200 feet of fencing. The optimal solution is a square pen measuring 300 feet on each side, yielding a maximum area of 90,000 square feet. Additionally, Problem #25 involves analyzing a set of points to identify their characteristics, including determining the domain and range of the given coordinates.

PREREQUISITES
  • Understanding of basic geometry concepts, including perimeter and area calculations.
  • Familiarity with quadratic equations and their applications in maximizing area.
  • Knowledge of coordinate systems and how to identify domain and range.
  • Ability to interpret graphical representations of mathematical problems.
NEXT STEPS
  • Study the derivation of the area formula for rectangles and squares.
  • Learn how to apply the quadratic formula to maximize area problems.
  • Explore the concepts of domain and range in relation to functions and graphs.
  • Practice constructing and interpreting diagrams for geometric problems.
USEFUL FOR

Students in mathematics, educators teaching geometry, and anyone interested in solving optimization problems involving area and perimeter.

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PROBLEM #24- A goat rancher is going to fence off a rectangular pen in the middle of a large open area. Build an equation to help determine the maximum area (to the nearest sq ft) that can be fenced off if 1200 ft of fencing is avilable. Include a diagram as a part of your solution.)

I have attached the two problems I need help with in picture format for number 24 and 25. I need to write an equation for 24 which I am having trouble with even though I know the answer is 90,000 sq ft
@ 300ft x 300ft.

On #25 I am not sure if this is a line, function, or if it even has a slope or pattern. How do I answer the questions beneath? Thanks.






 

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Someone please help here this is due tomorrow morning- thanks.
 
Ah, that is bad luck. They still haven't approved the image.
 
A goat rancher is going to fence off a rectangular pen in the middle of a large open area. Build an equation to help determine the maximum area (to the nearest sq ft) that can be fenced off if 1200 ft of fencing is avilable. Include a diagram as a part of your solution.
 
Ok so for #24 you need to build an equation to help find the maximum area. It says that perimeter is 1200ft. What kind of equations can you think of that would be helpful? How about the equation for perimeter and area? If you find those two equations you are finished.
 
For problem 25 you say you are "not sure if this is a line, function, or if it even has a slope or pattern". It is precisely the points shown: (-2, 5), (-1, 3), (1, 0), (3, -3), and (4, -5).

The "domain" is the set of all "x" values- all first numbers in the pairs.
The "range" is the set of all "y" values- all second numbers in the pairs.
 

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