Question

Value of x??????????????​

Answer 1

x = 3.5 units

Explanation:

Let h be the height of triangle.

`\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 * 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 = - (9)/(2) \: or \: x = (7)/(2) \\ but \: x \: can \: not \: be \: - ve \\ \therefore \: x \\eq \: - (9)/(2) \\ \therefore \: x = (7)/(2) \\ \huge \red{ \boxed{ \therefore \: x = 3.5 \: units}}`