Final answer:
The dimensions of the air hockey table are determined by solving the equations derived from the area (40 square feet) and the perimeter (28 feet). After factoring the quadratic equation, we find that the dimensions are 10 feet by 4 feet, which corresponds to option A.
Step-by-step explanation:
To find the dimensions of the air hockey table, we use the given area and perimeter. The area (A) of a rectangle is length × width, and the perimeter (P) is 2 × (length + width). We are given that A = 40 square feet and P = 28 feet.
Let's denote the length as L and the width as W. We have two equations to solve for two variables:
- A = L × W
- P = 2 × (L + W)
From the perimeter equation, we can express one variable in terms of the other:
28 = 2 × (L + W) → L + W = 14 → W = 14 - L
Substitute W into the area equation:
40 = L × (14 - L)
Now, solve for L:
L² - 14L + 40 = 0
By factoring, we get:
(L - 10)(L - 4) = 0
Hence, L = 10 and W = 4, or L = 4 and W = 10. Therefore, the dimensions of the table are 10 feet by 4 feet, which matches option A.