Of course! Let's break down the problem step by step to find the correct answer.

Problem Summary:

You're asked to determine how much space is in your apartment based on the given blueprint. The dimensions in the blueprint involve algebraic expressions.

The options for $a$ are:

1. $a = x + 24$
2. $a = x + 6$
3. $a = x + 48$
4. $a = x + 12$ (this one was selected but marked incorrect)

Diagram Analysis:

The blueprint shows two algebraic expressions:

• One side labeled as $3x - 10$
• Another side labeled as $2x^2 - 11x^2 - 16$

But the second expression seems to need simplification. Simplifying it:

$2x^2 - 11x^2 - 16 = -9x^2 - 16$

This doesn't directly relate to the side lengths. It’s possible the correct side lengths or area formula isn't fully shown.

Strategy:

• Double-check how the side lengths relate to $a$.
• Solve for $a$ algebraically.
• Compare results with the answer choices.

Would you like me to walk through solving it step by step or explain how to approach these kinds of problems? Let me know!

Here are 5 related questions to help strengthen your understanding:

1. How do you solve quadratic equations when simplifying expressions?
2. What is the difference between area and perimeter in algebraic expressions?
3. How do you expand and factor polynomials?
4. How can you verify if your algebraic answer is correct?
5. What strategies can you use to check multiple-choice math answers?

Tip: Always simplify algebraic expressions fully and double-check for calculation errors before choosing an answer.