The length of a rectangular flower garden is twice the width of the garden. The two shorter sides
and one of the longer sides have a two-foot wide walking path bordering the garden.

Part A: Draw the rectangle and side lengths.

Part B: Create a function where, A(x) represents the total area covered by the garden and the
walking path given x represents the width of the garden.

Part C. If the width of the garden is 3 feet, what is the total area of the garden and walking path?

SHOW ALL WORK

Step-by-step explanation: We shall start by labelling the rectangle ABCD. The dimensions are 2x and x, since we have been given that the shorter side is x, and the longer side is twice the length of the longer side.

In the diagram, the walkpath runs along the two shorter sides and one of the longer sides. The shaded region represents that walkpath that is not part of the rectangular garden. Therefore the total area covered by the garden and walkpath is represented by

Area of EFHI minus Area of EFGJ.

Area of a rectangle = L × W

In EFHI, length is 2x + 4 and width is x + 4

Area = (2x + 4) × (x + 4)

= 2x² + 8x + 4x + 16

= 2x² + 12x + 16

In EFGJ, length is 2x + 4 and width is 2

Area = (2x + 4) × 2

= 4x + 8

Therefore, the total area covered by the garden and the walking path is given by the function;

A = (2x² + 12x + 16) - (4x + 8)

= 2x² + 12x + 16 - 4x - 8

=2x² + 8x + 8

Part B; the function of the total area of the garden and the walkpath is given as

2x² + 8x + 8

Part C; if the width of the garden is 3 ft, then

x = 3

Therefore the total area of the garden and the walkpath is

Substitute for the value of x in the Area

=2x² + 8x + 8

=2(3)² + 8(3) + 8

=2(9) + 24 + 8

= 18 + 24 + 8

= 50ft.