# Find the possible dimensions for each garden

• MHB
• Yazan975
In summary, the conversation discusses the dimensions of Emily's and Sarah's gardens, with Emily's garden being x by x+4 and Sarah's garden being y by 18. It is stated that the two gardens are similar, meaning that x/x+4 = y/18. This leads to the equation 18x = x^2+8x+16, which can be simplified to x^2-10x+16=0. From there, it is found that x can be either 2 or 8.
Yazan975
View attachment 8403

What I did:
x = Emily's garden's width
x+4 = Emily's garden's length

y= Sarah's garden's width
18 = Sarah's garden's length

y=x+4(as stated in problem)

x/x+4 = y/18(as the two gardens are similar)
Which means that x/x+4 = x+4/18

Now I can't seem to find x

#### Attachments

• Screen Shot 2018-09-14 at 2.31.48 PM-min.png
108 KB · Views: 62
$$\frac{x}{x+4}=\frac{x+4}{18}\implies18x=x^2+8x+16$$

Can you now find $x$?

greg1313 said:
$$\frac{x}{x+4}=\frac{x+4}{18}\implies18x=x^2+8x+16$$

Can you now find $x$?

Actually that's where I got to and couldn't go any further

$$18x=x^2+8x+16$$

$$x^2-10x+16=0$$

$$(x-2)(x-8)=0$$

$$x=2\text{ or }x=8$$

greg1313 said:
$$18x=x^2+8x+16$$

$$x^2-10x+16=0$$

$$(x-2)(x-8)=0$$

$$x=2\text{ or }x=8$$

Thank you so much!

## 1. What do you mean by "possible dimensions" for a garden?

By possible dimensions, we mean the various combinations of length and width that can be used to create a garden space.

## 2. How do you determine the possible dimensions for a garden?

The possible dimensions for a garden can be determined by considering factors such as available space, desired shape, and practicality.

## 3. Are there any standard dimensions for a garden?

No, there are no standard dimensions for a garden as it can vary greatly depending on individual preferences and available space.

## 4. Can the dimensions of a garden affect its growth and productivity?

Yes, the dimensions of a garden can influence its growth and productivity. For example, a larger garden may allow for more plants to be grown, while a smaller garden may require more careful planning and spacing of plants.

## 5. Is it better to have a rectangular or square garden?

The shape of a garden is a matter of personal preference. Both rectangular and square gardens can be equally productive, as long as they are well-designed and maintained.

• General Math
Replies
1
Views
2K
• General Math
Replies
6
Views
2K
• General Math
Replies
1
Views
845
• General Math
Replies
9
Views
1K
• Mechanics
Replies
32
Views
4K
• General Math
Replies
3
Views
763
• General Math
Replies
2
Views
778
• General Math
Replies
1
Views
837
• General Math
Replies
10
Views
1K
• Earth Sciences
Replies
27
Views
14K