Answer:
x = 3.5 units
Step-by-step explanation:
Let h be the height of triangle.
[tex] \therefore \: {h}^{2} = (2x + 1)^{2} - {8}^{2} \\ \hspace{24 pt}= 4 {x}^{2} + 4x + 1 - 64 \\ \hspace{24 pt}= 4 {x}^{2} + 4x - 63 ...(1)\\ \\ by \: geometric \: mean \: property \\ {h}^{2} = 8 \times x \\ {h}^{2} =8x...(2) \\ from \: equations \: (1) \: and \: (2) \\ 4 {x}^{2} + 4x - 63 = 8x \\ \therefore \: 4 {x}^{2} + 4x - 63 - 8x = 0 \\ \therefore \: 4 {x}^{2} - 4x - 63 = 0 \\ \therefore \: 4 {x}^{2} + 18x - 14x - 63 = 0 \\ \therefore \: 2x(2x + 9) - 7(2x + 9) = 0 \\ \therefore \: (2x + 9)(2x - 7) = 0 \\ \therefore \: 2x + 9 = 0 \: or \: 2x - 7 = 0 \\ \therefore \: x = - \frac{9}{2} \: or \: x = \frac{7}{2} \\ but \: x \: can \: not \: be \: - ve \\ \therefore \: x \neq \: - \frac{9}{2} \\ \therefore \: x = \frac{7}{2} \\ \huge \red{ \boxed{ \therefore \: x = 3.5 \: units}}[/tex]
