Question 1160125: A rectangular garden is surrounded by a walk of uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards (height by base), find the dimensions of the garden. What is the height?
Found 3 solutions by mananth, greenestamps, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
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A rectangular garden is surrounded by a walk of uniform width.let it be x yards
The area of the garden is 180 square yards.
the dimensions of the garden plus the walk are 16 yards by 24 yards
length of garden = 16-2x
width of garden = 24-2x
Area of garden = L * W
(16-2x)(24-2x) =180
384-32x-48x+4x^2= 180
simplify
4x^2-80x +204=0
divide by 4
x^2-20x+51=0
x^2-17x-3x+51=0
x(x-17)-3(x-17) =0
(x-17)(x-3) =0
x=17 or 3
x cannot be 17
so x=3
Length 16-6= 10
24-6 =18
Garden cannot have height . It has length and width.
Dimensions of garden = 10 & 18 yards
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
(1) Although it is unusual, you can call the dimensions of the garden base and height....
(2) If an algebraic solution is not required, this problem can be solved in a few seconds with logical reasoning and a bit of easy mental arithmetic.
For the garden plus walk, the difference between the two dimensions is 8 yards.
Since the walk is uniform width, the difference between the dimensions of the garden alone is also 8 yards.
So the task is to find two numbers with a product of 180 and a difference of 8.
Almost immediately the two numbers 18 and 10 should be seen.
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
Hello,
(1) if you ask about the dimensions of the garden, stop at this point.
Do not extend your curiosity further and do not ask again about the "height".
It is just EXCESSIVE.
(2) if you talk about a garden, do not use the terms "the base" and "the height", since they are not applicable to a garden.
Keep your terminology consistent.
Math is a harmony . . .
Language is a harmony, as well.
Math problem formulation must radiate a harmony, too.
By the way, it is a NECESSARY condition for young students to fall in love to Math.
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