Question

geometry a rectangular swimming pool is surrounded by a concrete sidewalk that is 3 feet wide. the dimensions of the rectangle created by the sidewalk are 21 feet by 31 feet. a. which equation represents the area of the sidewalk in square feet?

Explanation:

Step1: Find pool's length and width

The sidewalk is 3 ft wide on both sides. So, pool's length: \( 31 - 2\times3 = 31 - 6 = 25 \) ft. Pool's width: \( 21 - 2\times3 = 21 - 6 = 15 \) ft.

Step2: Area of sidewalk = total area - pool area

Total area (sidewalk + pool) is \( 31\times21 \). Pool area is \( 25\times15 \). So, sidewalk area equation: \( 31\times21 - (31 - 6)\times(21 - 6) \) (or \( 31\times21 - 25\times15 \)).

Answer:

The equation representing the area of the sidewalk is \( 31\times21 - (31 - 2\times3)\times(21 - 2\times3) \) (or simplified as \( 31\times21 - 25\times15 \)).