Question

question 6 of 10
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 new weight room has an area of 480 ft².
b. the new weight room has an area of $4x^2$ ft².
c. the gym has an area of 480 ft².
d. the new weight room can hold 480 people.

Explanation:

1. First, recall the given areas: the gym's area is \(4x^{2}\) \(ft^{2}\), and the total area of gym and weight room is \((4x^{2}+480)\) \(ft^{2}\).
2. To find the area of the weight room, we subtract the gym's area from the total area: \((4x^{2}+480)-4x^{2}=480\).
3. Analyze the options:

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

Answer:

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