1. Rectangular Garden

A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length and width of the garden are to be the same length, what would be the dimension of the garden? What would be the area of the square garden?

Length = width = same

46 = (x + 4) + (x + 4)

46 = 2x + 8

46 - 8 = 2x

38 = 2x

38/2 = x

19 feet

The length and width are 19 feet.

The area is (19 * 19) or 361 ft^2.

Is this correct?

2. Re: Rectangular Garden Originally Posted by harpazo A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length and width of the garden are to be the same length, what would be the dimension of the garden? What would be the area of the square garden?

Length = width = same
I am not sure what this was supposed to mean! Yes, the problem says that "length" and "width" are equal but "same" is not a number.
It would be better to say "length= width= x" since you use x to represent their common value.

46 = (x + 4) + (x + 4)
And you have a major mistake here! The garden has four sides to be fenced, not just 2!

46 = 2x + 8

46 - 8 = 2x

38 = 2x

38/2 = x

19 feet

The length and width are 19 feet.

The area is (19 * 19) or 361 ft^2.

Is this correct?

3. Re: Rectangular Garden

IF the whole 46 feet was used for the garden only,
then each side = 46/4 = 11.5, so area would be only 11.5 * 11.5 = 132.25.
That's a far cry from your 361.

Kind suggestion: try and check any answer you get for "reasonability".

"A gardener has 46 feet of fencing to be used to enclose a rectangular garden".
The teacher that wrote that deserves a good kick in the ass: why not simply say "a square garden"?!!!

4. Re: Rectangular Garden Originally Posted by harpazo A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.
If the length and width of the garden are to be the same length, what would be the dimension [sic]of the garden? What would be the area of the square garden?
1) This problem mentions "square garden" at the end, but "rectangular garden" prior to that.

2) The problem mentions a border surrounding the garden, even with a specific width, but that information is not used for the solution.

3) The word "length" is used in the same sentence as a name of one of the dimensions and also to mean how long something is. Two
different words would have been clearer/would have read more easily.

5. Re: Rectangular Garden

I believe the instructor was looking for:

Let $x$ be the length of one of the sides of the garden. The fencing adjacent to each side must be of length $x+4$ (to account for the two-foot-wide walkway/border surrounding the garden). We have:

$$46 = 4(x+4) \Longrightarrow x = \dfrac{15}{2} = 7.5$$

So, the garden has dimension $7.5\text{ ft.}\times 7.5\text{ ft}$ while the area is $\dfrac{225}{4}=56.25\text{ ft}^2$

This appears to be the same answer that HallsofIvy was suggesting, although I agree the problem is worded very poorly.

6. Re: Rectangular Garden Originally Posted by HallsofIvy I am not sure what this was supposed to mean! Yes, the problem says that "length" and "width" are equal but "same" is not a number.
It would be better to say "length= width= x" since you use x to represent their common value.

And you have a major mistake here! The garden has four sides to be fenced, not just 2! Originally Posted by greg1313 1) This problem mentions "square garden" at the end, but "rectangular garden" prior to that.

2) The problem mentions a border surrounding the garden, even with a specific width, but that information is not used for the solution.

3) The word "length" is used in the same sentence as a name of one of the dimensions and also to mean how long something is. Two
different words would have been clearer/would have read more easily. Originally Posted by DenisB IF the whole 46 feet was used for the garden only,
then each side = 46/4 = 11.5, so area would be only 11.5 * 11.5 = 132.25.
That's a far cry from your 361.

Kind suggestion: try and check any answer you get for "reasonability".

"A gardener has 46 feet of fencing to be used to enclose a rectangular garden".
The teacher that wrote that deserves a good kick in the ass: why not simply say "a square garden"?!!!
This problem is found in Section 1.7 in Michael Sullivan's College Algebra Ninth Edition.

7. Re: Rectangular Garden

Thank you everyone.