a rectangular flower garden, 7m by 6m is surrounded by a grass strip of uniform width.?

Question

of uniform width. if the total area of the garden and the grass strip is 90m^2, what is the width of the strip?




include a diagram, if possible

Answer 1

Area of flower garden 7 x 6m = 42sm
total area of both = 90sm
area of grass = 48sm
if 'w' is width of the strip then the area can be written in terms of length and width around the flower garden:
each long side, 2 of : (w + 7 +w) x w (the w's with the 7 is for the corners), plus
each short side, 2 of: 6 x w (don't count the corners again)
grass = 2 x (7w + 2w^2+ 6w) = 48sm
4w^2 + 26w =48 turn into quadratic
4w ^2+ 26w - 48 =0
w= (-26 +/- sqroot (26^2 -4x4x-48))/2x4
w= (-26 +/- sqroot (676+768)/8
w= (-26 +/- 38)/8
either w=(-64/8) = -8m (negative solution)
or w=(12/8) = 1.5m wide correct solution for the problem

Answer 2

Some number x has to be added to the width and the length to increase the area to 90. The equation for that is:

(7+x) * (6+x) = 90
42 + 6x + 7x + x^2 = 90
x^2 +13x - 48 = 0
(x - 3)(x + 16) = 0
x = 3 or -16 (but -16 can't be a size, so 3 is the only possible answer)

BUT, 3m is what is added in each direction, so you need half of that size on each side. The width of the strip is 1.5m.

Answer 3

Let the width of the strip be x metres.
Then the increased width is 6 + 2x metres, and the increased length is 7 + 2x metres.
The new area is (7 + 2x)(6 + 2x) m^2.
Therefore:
(7 + 2x)(6 + 2x) = 90
42 + 26x + 4x^2 - 90 = 0
4x^2 + 26x - 48 = 0
2(x^2 + 13x - 24) = 0
2(2x - 3)(x + 8) = 0
x = -8 or 3/2.
Discarding the negative root, the width of the strip is 1.5m.

Answer 4

Let width of strip be x m
length of garden + strip = 7 + 2x
breadth of garden + strip = 6 + 2x
(7 + 2x).(6 + 2x) = 90
42 + 26x + 4x² = 0
4x² + 26x - 48 = 0
2x² + 13x - 24 = 0
(2x - 3).(x + 8) = 0

Accept +ve value of x = 1.5
Width of strip is 1.5 m

Answer 5

3 meters

7+3 = 10
6 + 3 = 9

9x10 = 90 m^2