Answer:
5
Step-by-step explanation:
Given is a right angled triangle.
Therefore, by Pythagoras theorem:
[tex] {(2x + 3)}^{2} = {x}^{2} + {(2x + 2)}^{2} \\ 4 {x}^{2} + 9 + 12x = {x}^{2} + 4 {x}^{2} + 4 + 8x \\ 9 + 12x = {x}^{2} + 4 + 8x \\ {x}^{2} + 4 + 8x - 12x - 9 = 0 \\ {x}^{2} - 4x - 5 = 0 \\ ({x}^{2} - 4x + 4 )- 4 - 5 = 0 \\ {(x - 2)}^{2} - 9 = 0 \\ {( x - 2)}^{2} = 9 \\ x - 2 = \pm \: \sqrt{9} \\ x - 2 = \pm 3 \\ x = 2 \pm 3 \\ x = 2 + 3 \: \: or \: \: x = 2 - 3 \\ x = 5 \: \: or \: \: x = - 1 \\ \because \: x \: can \: not \: be \: negative \\ \therefore \: x \neq \: - 1 \\ \therefore \: x = 5[/tex]
