A rectangular garden is to be surrounded by a walkway of constant width. The garden dimensions are 30 ft by 40

Question

ft. The total area, garden plus walkway, is to be 1800 ft.*2. What must be the width of thwe walkway to the nearest thousandths?

Answer 1

The area of the garden is 1200sq feet and therefore the area of the path is 600sq feet.

I'll do the rest and be back.

I'm back! Sorry, no calculator so only approx available.

(40+X)(30+X) = 1800 (Where X = 2x width of path)
X*2 + 70X + 1200 = 1800
X*2 + 70X - 600 = 0
Solve for X (X - 7.72)(X + 77.2) = 0

X = 7.72 as a widith of -77.2 would be meaningless.

The width of the path is 3.86 feet.

Do the rest your self.

Answer 2

The garden's area is 30 * 40 = 1200.

From the way the question is phrased, the walkway has a constant width, thus, you can calculate the new area as:
(30 + 2w) * (40 + 2w) = 1800, using 2 w because the walkway is on both sides.

(30 + 2w) * (40+2w) = 1800
30 * 40 + 30 * 2w + 40 * 2w + 2w * 2w = 1800
4w^2 + 140w + 1200 = 1800
w^2 + 35w - 150 = 0 (simplify and divide by 2)

Now, use the quadratic formula:
w = (-b +/- (b^2-4ac)^1/2)/2a
w = (-35 +/- (1225 + 600)^1/2)/2
w = -17.5 +/- ((1825)^/1/2)/4
w = -17.5 +/- 21.36
w = 3.86 ft (the other answer is negative). (Solution!)

Check:
(30 + 2w) * (40 + 2w) = 1800
(30 + 7.72) * (40 + 7.72) = 1799.9984 (check!)

Answer 3

let the width of the walkway be "x"
Thus, the dimension of the garden plus the walkway is (40 + 2x) by (30 + 2x)

It is known that the total area of garden plus walkway = 1800*2 ft.
Thus,

1800*2 = (40+2x) multiply by (30+2x)
3600 = 1200 + 80x + 60x + 4x^2
0 = 4x^2 + 140x + 1200 - 3600
0 = 4x^2 + 140x - 2400
Then, simplify the equation by dividing it with 4
0 = x^2 + 35x - 600
Then, factorize the equation

X1 = -35+sqrt(35^2 - 4 (1) (-600))
-------------------------------------
2 (1)

= -35 +60.21
---------------
2
= 12.60 ft (Final Answer)

X2 = -35-sqrt(35^2 - 4 (1) (-600))
-------------------------------------
2 (1)
X2 = -35 - 60.21
--------------
2
X2 = -47.61 ft (can't use this since it has a negative value)

Hope it helps

Answer 4

1800*2=3600
30*40=1200
3600-1200=2400 area of walkway
(30*2)+(40*2)=140 perimeter of garden
that should get you going. good luck

Answer 5

Do your own homework!!!!