A garden area is 30 feet long and 20 feet wide. A path of uniform width is set around th edge. If the remaining garden area is 400 ft^2, what is the width of the path?
2006-10-03 12:41:04 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
If the path width is x, then the "remaining garden" dimensions are:
Length: 30 - 2x
Width: 20 - 2x
So, solve for this:
(30 - 2x)(20 - 2x) = 400
2006-10-03 12:43:45 · answer #1 · answered by PJ 3 · 0⤊ 0⤋
Total area of the garden is 600 sq ft. Remaining garden= 400sq ft, So the total area of the path is 200 Sq ft.
200 = 2(20x) + 2(30-2X)x So what does this say?
x = path width
200 (Area of the path)= (the 2 sides that are 20ft, times some value x) + 2 (times the thirty foot sides minus two times the path width( this is the tricky part, we have to subtract two times the width of the path from the 20x sides here from the thirty foot sides) times x
200 = 2(20x) + 2(30-2X)x
200=40x + (60 - 4x )x
200 = 40x + 60x - 4x2 note: 4x2 means 4x squared
To use the quadratic formula we need to have one side =0 so,
200 -40x -60x +4x2 =0 this can now be re-written to use in our quadtatic formula as 4x2 - 100x +200 =0
In the quadratic formula a=the coefficient of the squared term, in this case it is 4. b= the coefficient of the x term, in this problem that's -100. and the c is = to the number which has no x term associated with it, here that number is 200.
so a=4, b= -100, and c=200. CAREFULLY!! plug these numbers into the quadratic formula and you will get the answer. It should come out to 2.192 if you do it correctly.
2006-10-03 23:10:17 · answer #2 · answered by waldon l 2 · 0⤊ 0⤋
You don't need any quadratics here.
30 x 20 = 600 ft^2
There must be 200 ft^2 of path since only 400 ft^2 of garden remain.
You know that the path is uniform, so the width will be uniform.
30+20+20+30 = 100 ft
Width must be 2ft to make 200ft^2.
Double check this:
(30 x 2) + (20 x 2) + (20 x 2) + (30 x 2) = 60+40+40+60 = 200
Regards,
Mysstere
2006-10-03 19:47:03 · answer #3 · answered by mysstere 5 · 0⤊ 1⤋
(30-2x)(20-2x)=400
solve for x.
2006-10-03 19:43:39 · answer #4 · answered by Jimee77 4 · 0⤊ 0⤋
sorry i took algebra like 3 months ago and i still have no idea how to do that
2006-10-03 19:42:51 · answer #5 · answered by bri 2 · 0⤊ 1⤋
x = -b +/- the square root of b(squared)- 4ac all over 2a....
my best guess is 7...i hate algebra
2006-10-03 19:43:51 · answer #6 · answered by Anonymous · 0⤊ 1⤋
3.3
2006-10-03 19:46:24 · answer #7 · answered by markus 2 · 0⤊ 1⤋