A swimming pool manufacturer installs rectangular pools whose length is twice the width, plus 5m. Find a simplified algebraic expression that describes the total length of coping needed. Include a labelled diagram in your solution for full marks.
L = (2 w+5)
perimeter =2 L + 2 w
= 2*(2w+5) + 2 w
= 4 w+ 10 + 2 w
= 6 w + 10
Let's assume the width of the rectangular pool is "w" meters.
According to the given information, the length of the pool is twice the width, plus 5 meters. Therefore, the length can be expressed as:
Length = 2w + 5 meters
Now, let's define "c" as the coping needed along the width and "d" as the coping needed along the length. Since there are two widths and two lengths in a rectangular pool, the total length of coping needed can be expressed as:
Total Length of Coping = 2c + 2d
To determine the dimensions of the coping needed, we can consider the diagram shown below:
```
----------------------------------------------------
| d |
| |
| d |
| |
|-------- c ------ ... ------- c ----------|
| |
| |
| |
|--------------------------- w ----------------|
```
From the diagram, we can observe that the coping along the length is equal to the length of the pool (2w + 5 meters). Similarly, the coping along the width is equal to the width of the pool (w meters). Therefore, we can substitute these values into the equation for the total length of coping needed.
Total Length of Coping = 2c + 2d
= 2(w) + 2(2w + 5)
= 2w + 4w + 10
= 6w + 10
Thus, the simplified algebraic expression that describes the total length of coping needed is 6w + 10 meters.
To find a simplified algebraic expression for the total length of coping needed for the rectangular pool, let's first understand what coping is. Coping is the material placed around the edges of a swimming pool to provide a finished look and help secure the pool structure.
Let's start solving this problem step by step.
Step 1: Understanding the problem
According to the problem, the length of the rectangular pool is twice the width plus 5 meters. Let's assume that the width of the pool is 'w' meters. Therefore, the length of the pool would be 2w + 5 meters.
Step 2: Defining the terms
To make it easier to find the expression, let's assign labels to the variables.
Let:
- 'w' represent the width of the pool.
- 'L' represent the length of the pool.
Step 3: Formulating the expression
From the problem statement, we know that the length of the pool is 2 times the width plus 5 meters.
So, we can write the equation as:
L = 2w + 5
The total length of coping needed would be the perimeter of the rectangular pool, which is the sum of all four sides.
Since we have the formulas for the length and width, we can use them to calculate the perimeter.
Perimeter = 2(length + width)
Substituting the values from our equations, we get:
Perimeter = 2(2w + 5 + w)
Perimeter = 2(3w + 5)
Perimeter = 6w + 10
Therefore, the simplified algebraic expression for the total length of coping needed is 6w + 10.
Here is a labeled diagram of the rectangular pool:
______________________
| |
| |
w | | w
| |
| |
|______________________|
In the diagram, 'w' represents the width of the rectangular pool, and the sides labeled 'w' are the width sides, while the sides labeled '2w + 5' are the length sides.
I hope this explanation helps! Let me know if you have any further questions.