Question

1. a rectangular pool 6 meters by 8 meters is to be surrounded by a walkway of width x meters. this problem has to do with the rectangular region taken up by the pool and walkway.

(c) what is the area of the full rectangular region when x = 3?
fill in the missing value:
the area of the full region when x = 3 is square meters.

Explanation:

Step1: Determine new dimensions

The pool is 6m (length) and 8m (width). The walkway has width \( x \). So the new length of the full region is \( 6 + 2x \) (since walkway is on both sides) and new width is \( 8 + 2x \).

Step2: Substitute \( x = 3 \)

Substitute \( x = 3 \) into the length and width formulas.
New length: \( 6 + 2(3) = 6 + 6 = 12 \) meters.
New width: \( 8 + 2(3) = 8 + 6 = 14 \) meters.

Step3: Calculate area

Area of a rectangle is \( \text{length} \times \text{width} \). So area \( = 12 \times 14 = 168 \) square meters.

Answer:

168