Question

a rectangular gym has an area of $4x^2$ ft². the school decides to add a new weight room. the total area of the gym and the weight room is $(4x^2 + 480)$ ft². what does the constant term represent in terms of this problem? a. the gym has an area of 480 ft². b. the new weight room can hold 480 people. c. the new weight room has an area of 480 ft². d. the new weight room has an area of $4x^2$ ft².

Explanation:

Step1: Analyze the given areas

The gym's area is \(4x^{2}\) \(ft^{2}\), and the total area of gym and weight room is \((4x^{2}+480)\) \(ft^{2}\).

Step2: Determine the weight room's area

To find the weight room's area, subtract the gym's area from the total area: \((4x^{2}+480)-4x^{2}=480\) \(ft^{2}\). So the constant term 480 represents the weight room's area.

Step3: Evaluate the options

• Option A: The gym's area is \(4x^{2}\), not 480, so A is wrong.
• Option B: The problem is about area, not the number of people, so B is wrong.
• Option C: As calculated, the weight room's area is 480 \(ft^{2}\), so C is correct.
• Option D: The weight room's area is 480, not \(4x^{2}\), so D is wrong.

Answer:

C. The new weight room has an area of \(480\space ft^{2}\).