Domanda del libro di testo
Exercises 57–59 will help you prepare for the material covered in the next section. Subtract:
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Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 6, Problema 58
Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.
Guida verificata passo dopo passo1
Let the length of the rectangle be \(L\) feet and the width be \(W\) feet. We are given two conditions: the perimeter and the area.
Write the equation for the perimeter of a rectangle: \(2L + 2W = 40\). Simplify this to \(L + W = 20\).
Write the equation for the area of a rectangle: \(L \times W = 96\).
From the perimeter equation, express one variable in terms of the other, for example, \(L = 20 - W\).
Substitute \(L = 20 - W\) into the area equation to get \((20 - W) \times W = 96\). This will give a quadratic equation in terms of \(W\) that you can solve.
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Perimeter of a Rectangle
The perimeter of a rectangle is the total distance around it, calculated as P = 2(length + width). This formula helps relate the length and width when the perimeter is known, providing one equation to solve for the dimensions.
Area of a Rectangle
The area of a rectangle is the amount of space inside it, found by multiplying length by width (A = length × width). Knowing the area gives a second equation that, combined with the perimeter, allows solving for both dimensions.
Video consigliato:
6:19
Systems of Inequalities
Solving Systems of Equations
To find the length and width, you set up two equations from the perimeter and area formulas and solve them simultaneously. Techniques include substitution or elimination, which help find the values of length and width that satisfy both conditions.
Video consigliato:
5:48Solving Systems of Equations - Substitution
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