Quadratic equations: Perimeter and Area fencing dimensions

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SUMMARY

The discussion focuses on solving a quadratic equation related to determining the dimensions of a rectangular enclosure with a perimeter of 280 meters and an area of 2800 square meters. The key equations involved are the perimeter equation \( P = 2L + 2W \) and the area equation \( A = L \times W \). By substituting the perimeter into the area equation, the dimensions can be calculated using the quadratic formula \( x = \frac{-b ± \sqrt{b^{2}-4ac}}{2a} \). The solution yields the length and width of the enclosure to the nearest tenth.

PREREQUISITES
  • Understanding of quadratic equations and their applications.
  • Familiarity with perimeter and area formulas for rectangles.
  • Knowledge of algebraic manipulation and substitution methods.
  • Ability to use the quadratic formula for solving equations.
NEXT STEPS
  • Practice solving quadratic equations using the quadratic formula.
  • Explore applications of perimeter and area in real-world scenarios.
  • Learn about optimization problems in geometry.
  • Investigate different shapes and their area and perimeter relationships.
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Students studying geometry, mathematics educators, and anyone interested in applying algebra to solve real-world fencing and enclosure problems.

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Homework Statement


The following enclosure is built using 280 m of fencing. If the enclosure has a total area of 2800 m2, what are the dimensions to the nearest tenth?

Homework Equations


x = \frac{-b ± \sqrt{b^{2}-4ac}}{2a}


The Attempt at a Solution


Please note that the 3/2w and 5/2w were measurements I did with a ruler. I am pretty sure that is wrong since this question is not suppose to require manual measurements.

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Assume the enclosure is L long and W wide.

What is the amount of fencing used, in terms of W and L?
What is the area of the enclosure, in terms of W and L?
 

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