So with this, we will be using proportions. To solve for x, our proportion will be [tex] \frac{x}{6} =\frac{6}{x-9} [/tex]
Firstly, cross-multiply: [tex] x^2-9x=36 [/tex]
Next, subtract 36 on both sides: [tex] x^2-9x-36=0 [/tex]
Next, replace -9x with 3x-12x [tex] x^2+3x-12x-36=0 [/tex]
Next, factor x^2+3x and -12x-36 separately: [tex] x(x+3)-12(x+3)=0 [/tex] . After, rewrite it as [tex] (x-12)(x+3)=0 [/tex]
Next, solve for x separately in the two parentheses:
[tex] x-12=0\\ x=12 [/tex]
[tex] x+3=0\\ x=-3 [/tex]
Since we can't have a negative length, x = 12.
To solve for y, our proportion will be [tex] \frac{y}{9} =\frac{12}{y} [/tex]
Firstly, cross-multiply: [tex] y^2=108 [/tex]
Next, just square root each side, and your answer will be (rounded to hundredths) [tex] y=10.39 [/tex]
In short, x = 12 and y = 10.39.
