Find the possible dimensions for each garden

[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

 

[Greg]

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

Can you now find $x$?

 

[Yazan975]

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

Can you now find $x$?

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

 

[Greg]

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

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

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

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

 

[Yazan975]

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

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

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

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

Thank you so much!