Quadratic equations: Perimeter and Area fencing dimensions

In summary, the problem involves finding the dimensions of an enclosure with a total area of 2800 m2 and a perimeter of 280 m. To solve this, we can use the equation x = \frac{-b ± \sqrt{b^{2}-4ac}}{2a} and assume the enclosure has a length of L and a width of W. The amount of fencing used can be expressed as 3/2W + 5/2W + 2L = 280, and the area of the enclosure can be expressed as LW = 2800.
  • #1
Swan
16
0

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 = [itex]\frac{-b ± \sqrt{b^{2}-4ac}}{2a}[/itex]


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.

03.24.2013-15.15.png
 
Physics news on Phys.org
  • #2
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?
 

FAQ: Quadratic equations: Perimeter and Area fencing dimensions

What is a quadratic equation?

A quadratic equation is a mathematical equation with the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is called quadratic because the highest power of x is 2. Quadratic equations are commonly used to solve problems involving areas, distances, and other physical quantities.

How are quadratic equations used to find perimeter and area fencing dimensions?

Quadratic equations can be used to find the dimensions of a rectangular area that has a given perimeter or to find the dimensions of a rectangular fence that encloses a given area. By setting up a quadratic equation with the area or perimeter as the dependent variable and the dimensions as the independent variables, we can solve for the unknown dimensions.

Can quadratic equations be used for irregularly shaped areas?

No, quadratic equations can only be used for regular shapes such as rectangles and squares. For irregularly shaped areas, other methods such as integration or approximation techniques may be used.

What are the steps for solving a quadratic equation for perimeter and area fencing dimensions?

The steps for solving a quadratic equation for perimeter and area fencing dimensions are as follows:1. Identify the given information (perimeter or area) and the unknown dimensions.2. Set up the quadratic equation using the given information and the unknown dimensions.3. Simplify the equation and put it in standard form (ax^2 + bx + c = 0).4. Use the quadratic formula or factoring to solve for the unknown dimensions.5. Check your solution by plugging in the values for the unknown dimensions into the original equation.6. Write the final solution with the correct units.

What are the practical applications of quadratic equations for perimeter and area fencing dimensions?

Quadratic equations for perimeter and area fencing dimensions are commonly used in real-world scenarios such as designing a garden, building a fence around a pool, or calculating the cost of materials for a rectangular construction project. These equations are also used in fields such as engineering, architecture, and landscaping to determine the most efficient use of space and resources.

Similar threads

Maximum area of a fenced-in half a circle
Replies
2
Views
2K
Perimeter/Area of Shaded Region within a Circle
Replies
10
Views
23K
Optimal Garden Shape for Minimizing Fencing
Replies
24
Views
5K
Finding the quadratic equation that suits the solutions
Replies
2
Views
1K
Teaching the quadratic equation and the roots
2
Replies
36
Views
5K
Solving a Quadratic Equation with Two Variables
Replies
6
Views
1K
Quadratic Formula (Equilibrium Points)
Replies
3
Views
2K
Find Rectangle Sides Given Perimeter & Area
Replies
10
Views
3K
Problem on quadratic polynomial.
Replies
33
Views
7K
Optimizing Fencing for a Rectangular Enclosure with a Fixed Wall
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top