Score:
0 of 1 point

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

Question

Score:
0 of 1 point

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 · Accepted Answer

Let's break down the problem step by step.

### (a) Identify what $$ x $$ and $$ y $$ should represent.

We need to define the variables for the dimensions of the rectangular deck.

- Let $$ x $$ represent the deck's length.
- Let $$ y $$ represent the deck's width.

Thus, the correct choice is:
**A**: $$ \boldsymbol{x}= $$ the deck's length. $$ \boldsymbol{y}= $$ 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 $$ P $$ of a rectangle is given by:

$$
P = 2(x + y)
$$

Given that the perimeter is 60 feet, we can set up the equation:

$$
2(x + y) = 60
$$

To simplify, we can divide both sides by 2:

$$
x + y = 30
$$

This is the mathematical representation of the first sentence.

Now we have:
1. $$ x + y = 30 $$ (perimeter equation)
2. The relationship between length and width: $$ x = 4y - 5 $$ (length is 5 feet less than four times the width).

Next, we can solve these equations to find the values of $$ x $$ and $$ y $$. Would you like me to proceed with solving these equations?
(a) $$ x $$ represents the deck's length, and $$ y $$ represents the deck's width. (b) The perimeter equation is $$ x + y = 30 $$.

Upstudy AI Solution

Answer

Solution

(a) Identify what and should represent.

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

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