Question
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The perimeter of a rectangular wooden deck is 60 feet. The deck’s length is 5 feet less than four times its width. We are interested in determining the length and the width of the deck.
Use the information provided to answer the following questions:
(a) Identify what and should represent in this case.
A the deck’s length. the deck’s width.
B the sum of length and width of the deck the deck’s shape.
c the deck’s width the deck.
D the deck’s perimeter
the deck’s shape.
(b) Translate the first sentence sentence: "perimeter of a wooden deck is 60 ", into a math equation.

Ask by Stuart Mills. in the United States
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

(a) represents the deck’s length, and represents the deck’s width.
(b) The perimeter equation is .

Solution

Let’s break down the problem step by step.

(a) Identify what and should represent.

We need to define the variables for the dimensions of the rectangular deck.
  • Let represent the deck’s length.
  • Let represent the deck’s width.
Thus, the correct choice is:
A: the deck’s length. the deck’s width.

(b) Translate the first sentence: “perimeter of a wooden deck is 60”, into a math equation.

The formula for the perimeter of a rectangle is given by:
Given that the perimeter is 60 feet, we can set up the equation:
To simplify, we can divide both sides by 2:
This is the mathematical representation of the first sentence.
Now we have:
  1. (perimeter equation)
  2. The relationship between length and width: (length is 5 feet less than four times the width).
Next, we can solve these equations to find the values of and . Would you like me to proceed with solving these equations?

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

The Deep Dive

To solve this problem, let’s think about the definitions of length and width clearly. In option A, we correctly identify as the deck’s length and as the deck’s width. This sets up our variables for a straightforward approach! The other options mix up concepts or don’t pertain to the dimensions we are seeking.
Now, for translating the perimeter condition into a mathematical equation: The perimeter of a rectangle is given by the formula . Since we know the perimeter is 60 feet, we can write the equation as . This simplifies to when we divide both sides by 2. This equation provides us a foundational piece to work with in our calculations!

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