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Question Number 83030 by Power last updated on 27/Feb/20

	Answered by mr W last updated on 27/Feb/20

	Commented by mr W last updated on 27/Feb/20

	${(a + b)}^{2} = a^{2} + {(2 a - b)}^{2}$ $\Rightarrow b = \frac{2}{3} a$ $\tan α = \frac{a}{2 a} = \frac{1}{2}$ $\tan β = \frac{b}{2 a} = \frac{1}{3}$ $\frac{C B}{\sin (45 + β)} = \frac{G B}{\sin β}$ $C B = 2 a = \frac{3 \sin (45 + β)}{\sin β} = 3 \times \frac{\sqrt{2}}{2} (1 + \frac{1}{\tan β})$ $\Rightarrow 2 a = \frac{3 \sqrt{2}}{2} (1 + 3) = 6 \sqrt{2}$ $\frac{D H}{\sin α} = \frac{D C}{\sin (45 + α)}$ $x = \frac{\sin α}{\sin (45 + α)} \times 2 a = \frac{\sqrt{2}}{1 + \frac{1}{\tan α}} \times 6 \sqrt{2}$ $x = \frac{\sqrt{2}}{1 + 2} \times 6 \sqrt{2} = 4$
	Commented by Power last updated on 27/Feb/20

	$thank you sir$
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