Thank you for visiting The area of the surface of a workbook is 48 square inches The perimeter is 28 inches What are the dimensions of the workbook. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The dimensions of the workbook are [tex]6[/tex] inches and [tex]8[/tex] inches.
To find the dimensions of the workbook given the area and perimeter, we can use the following formulas:
Area: The area of a rectangle is calculated using the formula:
[tex]A = l \times w[/tex]
where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
Perimeter: The perimeter of a rectangle is calculated using the formula:
[tex]P = 2(l + w)[/tex]
where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
Given:
Area [tex]A = 48[/tex] square inches
Perimeter [tex]P = 28[/tex] inches
Step 1: Set up the equations.
From the area equation:
[tex]l \times w = 48 \quad (1)[/tex]
From the perimeter equation:
[tex]2(l + w) = 28 \quad (2)[/tex]
Dividing this equation by 2 gives:
[tex]l + w = 14 \quad (3)[/tex]
Step 2: Solve the system of equations.
From equation (3), we can express [tex]l[/tex] in terms of [tex]w[/tex]:
[tex]l = 14 - w \quad (4)[/tex]
Step 3: Substitute equation (4) into equation (1).
Substituting [tex]l[/tex] from equation (4) into equation (1):
[tex](14 - w)w = 48[/tex]
Rearranging gives:
[tex]14w - w^2 = 48[/tex]
or
[tex]w^2 - 14w + 48 = 0[/tex]
Step 4: Solve the quadratic equation.
To factor this quadratic equation, we need two numbers that multiply to 48 and add up to -14. These numbers are -6 and -8. Thus, we can factor it as:
[tex](w - 6)(w - 8) = 0[/tex]
Setting each factor equal to zero gives us the possible widths:
[tex]w = 6 \quad or \quad w = 8[/tex]
Step 5: Find the corresponding lengths.
Using equation (4), if [tex]w = 6[/tex], then:
[tex]l = 14 - 6 = 8[/tex]
And if [tex]w = 8[/tex], then:
[tex]l = 14 - 8 = 6[/tex]
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Rewritten by : Jeany
