Question

a rectangular garden has a walkway around it. the area of the garden is 2(4.5x+1.5) the combined area of the garden and the walkway is 2.5(6x+4). Find the area of the walkway around the garden as the sum of two terms.

Answer 1

x=-1.16666666667 or x=-1.17

Explanation:

2(4.5x+1.5) = 9x+3

2.5(6x+4) = 15x+10

9x+3=15x+10 subtract 3 on both sides

9x=15x+7 subtract 15x on both sides

-6x=7 divide -6 on sides

x=-1.16666666667 or x=-1.17

Answer 2

answer:14x+14.5

The area of the walkway around is 26 x + 16 as the sum of two terms

Explanation:

A rectangular garden has a walkway around it

1. The area of the garden is 4(4.5 x + 1.5)

2. The combined area of the garden and the walkway is 5.5(8 x + 4)

We need to find the area of the the walkway

To find the area of the walkway by subtracting the area of the

rectangle from the combined area

The combined area = 5.5(8 x + 4) ⇒ simplify it

The combined area = 5.5(8 x) + 5.5(4)

The combined area = 44 x + 22

The area of the garden = 4(4.5 x + 1.5) ⇒ simplify it

The area of the garden = 4(4.5 x) + 4(1.5)

The area of the garden = 18 x + 6

Now subtract the area of the garden from the combined area

Area of the walkway = (44 x + 22) - (18 x + 6)

Area of the walkway = 44x + 22 - 18 x - 6

- Add like terms

Area of the walkway = (44 x - 18 x) + (22 - 6)

Area of the walkway = 26 x + 16