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[tex] \frac{cd}{9} = \frac{ac}{bc} \\ \frac{cd}{16} = \frac{bc}{ac} \\ \frac{9 \times \frac{ac}{bc} }{16} = \frac{bc}{ac} \\ \frac{9 {(ac)}^{2} }{bc} = 16 \times bc \\ 9 {(ac)}^{2} = 16 {(bc)}^{2} \\ { (\frac{ac}{bc} )}^{2} = \frac{16}{9} \\ \frac{ac}{bc} = \frac{4}{3} \: \: \: \: \: \: ac = \frac{4}{3} \times bc \\ {(ac)}^{2} - {(ad)}^{2} = {(bc)}^{2} - {(bd)}^{2} \\ {( \frac{4}{3} \times bc)}^{2} - {16}^{2} = {(bc)}^{2} - {9}^{2} \\ \frac{16}{9} \times {(bc)}^{2} - {(bc)}^{2} = {16}^{2} - {9}^{2} \\ \frac{7}{9} \times {(bc)}^{2} = 175 \\ {(bc)}^{2} = 225 \\ bc = 15 \\ ac = 20 \\ cd = 12[/tex]