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Question Number 191602 by ajfour last updated on 26/Apr/23

Commented by ajfour last updated on 26/Apr/23

$L o a d i s t o b e t a k e n f r o m A t o B .$ $I f s = h, f i n d h i n t e r m s o f a, b .$
	Answered by mr W last updated on 27/Apr/23

	$\sqrt{{(h + b)}^{2} + h^{2}} - (h + b) = \sqrt{a^{2} + b^{2}}$ $h^{2} - 2 h \sqrt{a^{2} + b^{2}} - (a^{2} + b^{2} + 2 b \sqrt{a^{2} + b^{2}}) = 0$ $h = \sqrt{a^{2} + b^{2}} + \sqrt{2 (a^{2} + b^{2} + b \sqrt{a^{2} + b^{2}}})$
	Commented by ajfour last updated on 27/Apr/23

	$\sqrt{a^{2} + b^{2}} + b + h = \sqrt{{(b + h)}^{2} + s^{2}}$ $\Rightarrow a^{2} + b^{2} + 2 (b + h) \sqrt{a^{2} + b^{2}} = h^{2}$ $h^{2} - 2 \sqrt{a^{2} + b^{2}} h - (a^{2} + b^{2}) - 2 b \sqrt{a^{2} + b^{2}} = 0$ $\Rightarrow$ $h = \sqrt{a^{2} + b^{2}} + \sqrt{2 (a^{2} + b^{2}) + 2 b \sqrt{a^{2} + b^{2}}}$
	Commented by ajfour last updated on 27/Apr/23

	$y e s s i r, t h a n k s .$
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