MHB Find the possible dimensions for each garden

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The discussion focuses on solving for the dimensions of two similar gardens belonging to Emily and Sarah. Emily's garden width is represented as x, with a length of x+4, while Sarah's garden has a fixed width of y and a length of 18. The relationship between the gardens is established through the equation x/x+4 = y/18, leading to the quadratic equation 18x = x^2 + 8x + 16. This simplifies to x^2 - 10x + 16 = 0, which factors to (x-2)(x-8) = 0, yielding possible values of x as 2 or 8. The thread concludes with gratitude for assistance in solving the problem.
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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
 

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

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!
 
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