since ΔQRS similar to ΔQRP, then
SR/QR = QR/PR
x/12 = 12/(3.5+x)
x(3.5+x) = 12²
x² + 3.5x = 144
x² + 3.5x - 144 = 0
[tex]x = \frac{ - 3.5 + \sqrt{ {3.5}^{2} + 4 \times 144} }{2} \\ = \frac{ - \frac{7}{2} + \sqrt{ \frac{49}{4} + 576} }{2} \\ = \frac{ - 7 + \sqrt{49 + 2304} }{4} \\ = \frac{ - 7 + \sqrt{2353} }{4} [/tex]
approximately 10.38
