Question

A rectangular garden has a walkway around it. The area of the garden is 6​(3.5x+1.5​). The combined area of the garden and the walkway is 7.5​(6x+5​). Find the area of the walkway around the garden as the sum of two terms.

Answer 1

To find the area of the walkway around the garden, subtract the area of the garden from the combined area. The area of the walkway is 24x + 28 + 0.5.

Step-by-step explanation:

To find the area of the walkway around the garden, we need to subtract the area of the garden from the combined area of the garden and the walkway. Let's first expand the expressions:

Area of the garden = 6(3.5x + 1.5) = 21x + 9

Combined area = 7.5(6x + 5) = 45x + 37.5

Now, we can calculate the area of the walkway by subtracting the area of the garden from the combined area:

Area of the walkway = Combined area - Area of the garden = (45x + 37.5) - (21x + 9) = 24x + 28.5

Therefore, the area of the walkway around the garden is 24x + 28.5, which can be written as the sum of two terms as 24x + 28 + 0.5.

Answer 2

`A_w=24x+28.5`

Step-by-step explanation:

The rectangular garden is surrounded by a walkway.

The combined area of both is 7.5(6x+5) and the area of the garden alone is 6(3.5x+1.5).

The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:

`A_w=7.5(6x+5) -(6(3.5x+1.5))`

Removing parentheses:

`A_w=45x+37.5 -21x-9`

Simplifying:

`\mathbf{A_w=24x+28.5}`