Width - Walkway

[Guest]

A flower garden is bordered by a gravel walkway of uniform width. Area of walkway is 3/5 of garden area.

Dimensions of garden - 18 x 30 feet.

Calculate width of walkway.

My partial solution:

Area = Length x Width.

Garden area - 18 x 30 = 540 sq. ft.

Walkway area - 540 x 3/5 = 324 sq. ft.


How do I continue ? Thanks.

[Guest]

I had omitted:

Perimeter = 2L + 2W

2(30) + 2(18) = 96 feet = perimeter of garden.

[Guest]

Please respond. Thanks.

[Guest]

walkway area =

2 x 18 x W
plus
2 x 30 x W
plus
4W^2
and that =
3/5 x 18 x 30

then solve the eqn for W

[Guest]

2 x 18 x W + 2 x 30 x W + 4W^2 = 3/5 x 18 x 30
36 x W + 60 x W + 4W^2 = 324
96 X W ^2 + 4W^2 = 324
100W^2 = 324
100W^2/100 = 324/100
W^2 = 3.24

I don't think that is not correct.

[Guest]

I don't think that is not correct - should be I don't think that is correct.

[Guest]

Please respond. Thanks again.

[Guest]

2 x 18 x W + 2 x 30 x W + 4W^2 = 3/5 x 18 x 30
36 x W + 60 x W + 4W^2 = 324
96 X W + 4W^2 = 324
4W^2 + 96W - 324 = 0
W^2 + 24W - 81 = 0
(W - 3)(W + 27) = 0

W = 3 OR W = -27

Valid answer is W = 3

[Guest]

"36 x W + 60 x W + 4W^2 = 324
96 X W + 4W^2 = 324"

I don't understand why the 96 was multiplied by one W.

Does the 4W^2 mean the 4 sides and the width x width for each side of walkway?

[Guest]

36xW plus 60xW is 96xW
36W plus 60W is 96W

36 Wellingtons Plus 60 Wellingtons is 96 Wellingtons

The 4 squares in the corners are W x W = W^2 in area each
and there are 4 of then so total area is 4W^2

[Guest]

I don't understand the reasoning for the 4 squares in the corners.

[Guest]

The walkway at each side is 30 x W and there are 2 of them
The walkway at top and bottom is 18 x W each so thats 2 bits.
We have so fat counted the sides and top and botton walkways and excluded the bits at the corners.....
That leaves 4 corner squares W x W so thats 4W^2 to add on

[Guest]

I understand it now. Thanks.