## One-Bedroom Apartment AnalysisConsider the following drawing of a one-bedroom apartment and the given mathematical functions. ### Mathematical Functions- \( a(x) = x^2 - x + 2 \)- \( b(x) = 6x + 6 \)- \( c(x) = x^2 - 10x + 5 \)- \( d(x) = 5x + 1 \)### Apartment DiagramThe diagram provided shows the layout of a one-bedroom apartment with the dimensions labeled as follows:- Length comprises of sections \(a(x)\) and \(b(x)\)- Width comprises of sections \(c(x)\) and \(d(x)\)The specific rooms within the apartment are:- **Dining Area**- **Kitchen**- **Laundry**- **Living Area**- **Bedroom**- **Closets**, and **Lin. (Linen Closet)**- **Bath (Bathroom)**### Questions1. **What is the difference in the length and width of the one-bedroom apartment shown above? (Simplify your answer completely.)** - Length: \(a(x) + b(x)\) - Width: \(c(x) + d(x)\) \[ \text{Difference} = \left| [a(x) + b(x)] - [c(x) + d(x)] \right| \]2. **Find the perimeter of the apartment. (Simplify your answer completely.)** - Perimeter: \(2 \times \left( (\text{Length}) + (\text{Width}) \right)\) \[ \text{Perimeter} = 2 \times \left([a(x) + b(x)] + [c(x) + d(x)]\right) \]Includes:- Two input boxes for students to input and simplify their final answers for parts (a) and (b).### Tasks- Provide the simplified expressions for both the difference in dimensions and the perimeter as the problem asks for completely simplified answers. By analyzing the given apartment dimensions and using the provided functions, students can practice algebraic simplification and real-world application of mathematical concepts in architectural contexts.

Name: ## One-Bedroom Apartment AnalysisConsider the following drawing of a
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: ## One-Bedroom Apartment AnalysisConsider the following drawing of a one-bedroom apartment and the given mathematical functions. ### Mathematical Functions- \( a(x) = x^2 - x + 2 \)- \( b(x) = 6x + 6 \)- \( c(x) = x^2 - 10x + 5 \)- \( d(x) = 5x + 1