Consider premium room in a hotel , the construction work is in progress , customer want a setup box near the Window and there should be 3 racks which is of identical size. Width of the complete setup box is and the length of the set up box is 4 times the width. We are given with 108 feet of wood for the construction. What are the dimension rack and the set up box?

To solve this, let's break down the problem step by step:

### 1. Understanding the setup box dimensions:
We are told:
- The **width** of the setup box is \( W \) (unknown).
- The **length** of the setup box is 4 times the width, i.e., \( L = 4W \).
- The total wood available for construction is 108 feet.

### 2. Calculating the perimeter of the setup box:
Since the total available wood is 108 feet, it suggests that the perimeter of the setup box must be equal to or use part of this amount. The perimeter \( P \) of a rectangle is given by:
\[
P = 2L + 2W
\]
Substitute \( L = 4W \) into the equation:
\[
P = 2(4W) + 2W = 8W + 2W = 10W
\]

We know that the total wood available is 108 feet, so:
\[
10W = 108
\]

Solve for \( W \):
\[
W = \frac{108}{10} = 10.8 \, \text{feet}
\]

Now, substitute \( W = 10.8 \) feet into the equation for the length \( L \):
\[
L = 4W = 4(10.8) = 43.2 \, \text{feet}
\]

So, the dimensions of the setup box are:
- **Width**: 10.8 feet
- **Length**: 43.2 feet

### 3. Determining the dimensions of the racks:
We are told that there are 3 racks of identical size inside the setup box. The width of the entire setup box is 10.8 feet, and the racks are arranged along this width.

If the racks are of equal width, then the width of each rack is:
\[
\text{Rack width} = \frac{W}{3} = \frac{10.8}{3} = 3.6 \, \text{feet}
\]

Since the length of the racks will match the length of the setup box, the length of each rack is:
\[
\text{Rack length} = 43.2 \, \text{feet}
\]

### Final Answer:
- **Dimensions of the setup box**: 10.8 feet (width) by 43.2 feet (length)
- **Dimensions of each rack**: 3.6 feet (width) by 43.2 feet (length)

Would you like further details or clarification on any part of this solution?

### 5 Related Questions:
1. What is the total area of the setup box?
2. If the racks were arranged vertically, how would the height affect the design?
3. How would the problem change if the available wood was 200 feet?
4. Can we fit more than 3 racks if the size of each rack changes? 
5. What happens if the width-to-length ratio is changed from 1:4 to 1:3?

### Tip:
Always ensure units are consistent when solving real-world geometry problems to avoid confusion during calculation!

Consider a premium room in a hotel, the construction work is in progress, the customer wants a setup box near the window, and there should be 3 racks of identical size. The width of the complete setup box is unknown, and the length of the setup box is 4 times the width. We are given 108 feet of wood for the construction. What are the dimensions of the rack and the setup box?

Learn how to find the dimensions of a setup box and racks for a hotel room using geometry and algebra. This problem involves calculating the perimeter of a rectangle and understanding ratios, using a total of 108 feet of wood for construction. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation