Question

I did some work but I still can't seem to find X.

Answer 1

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

`x = \frac{ - 3.5 + \sqrt{ {3.5}^(2) + 4 * 144} }{2} \\ = \frac{ - (7)/(2) + \sqrt{ (49)/(4) + 576} }{2} \\ = ( - 7 + √(49 + 2304) )/(4) \\ = ( - 7 + √(2353) )/(4)`

approximately 10.38