panjang PQ=6 cm , PR=RS=ST= 12 cm . hitung panjang SU ?

[tex]\displaystyle \text{titik potong RP dengan QT adalah }A\\\text{titik potong RS dengan QT adalah }U\\\\\frac{\text{ST}}{\text{RA}}=\frac{\text{US}}{\text{RU}}\\\frac{12}{\text{RA}}=\frac{12-\text{RU}}{\text{RU}}\\\frac{\text{RU}}{\text{RA}}=\frac{12-\text{RU}}{12}\\12\text{RU}=12\text{RA}-\text{RA}\cdot\text{RU}\\\text{RA}\cdot\text{RU}=12\text{RA}-12\text{RU}...(i)[/tex]

[tex]\displaystyle \frac{\text{ST}}{\text{AP}}=\frac{\text{US}}{\text{PQ}}\\\frac{12}{12-\text{RA}}=\frac{12-\text{RU}}{6}\\72=(12-\text{RU})(12-\text{RA})\\72=144-12\text{RA}-12\text{RU}+\text{RU}\cdot\text{RA}\\72=144-12\text{RA}-12\text{RU}+12\text{RA}-12\text{RU}\\-72=-24\text{RU}\\3=\text{RU}\\\\\text{US}=\text{RS}-\text{RU}\\\text{US}=12-3\\\boxed{\boxed{\text{US}=9\,\text{cm}}}[/tex]