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Question Number 177675 by cortano1 last updated on 08/Oct/22

Commented by HeferH last updated on 08/Oct/22

${i s n}^{'} t 10 ?$ $4 x^{2} + x^{2} = 100$ $x^{2} = 20$ $A = \frac{20}{2} = 10 u^{2}$
Commented by som(math1967) last updated on 08/Oct/22

$I s 10 a r e a ? o r l e n g t h o f s i d e ?$
Commented by HeferH last updated on 08/Oct/22

$t h e g r e e n t r i a n g l e h a s t h e s a m e h e i g h t a n d$ $b a s e, s o w e n e e d \frac{x^{2}}{2} (‘ ‘ x^{″} w o u l d b e t h e$ $o r a n g e s e g m e n t)$
Commented by cortano1 last updated on 08/Oct/22

$the request is green area$
	Answered by som(math1967) last updated on 08/Oct/22

	$l e t B D = D C = x$ $B D = D E ∴ ∠ E B D = 45 \Rightarrow ∠ B A C = 45$ $∴ B C = A C = 2 x$ $4 x^{2} + x^{2} = 10^{2}$ $\Rightarrow x = 2 \sqrt{5}$ $a r . o f △ B D E = a r . △ A E D$ $[∵ D i s m i d p t o f B C, D E ∥ A C$ $∴ E i s m i d p t o f A B]$ $a r o f △ B D E = \frac{1}{2} \times 2 \sqrt{5} \times 2 \sqrt{5}$ $= 10 s q u n i t$ $A_{g r e e n} = 10 s q u n i t$ $[I f A D = 10]$
	Commented by som(math1967) last updated on 08/Oct/22

	Commented by HeferH last updated on 08/Oct/22

	$s o r r y i f I m i s u n d e r s t o o d y o u r q u e s t i o n s i r,$ $t h e y h a v e t h e s a m e c o l o r s o {i t}^{'} s p r o b a b l y$ $t h a t w a y .$
	Commented by Tawa11 last updated on 08/Oct/22

	$Great sir$
	Answered by Ar Brandon last updated on 08/Oct/22

	$x^{2} + 4 x^{2} = 10^{2} \Rightarrow x = 2 \sqrt{5}$ $A = \frac{2 x \times 2 x}{2} - \frac{x \times 2 x}{2} - \frac{x \times x}{2}$ $= 2 x^{2} - x^{2} - \frac{x^{2}}{2} = \frac{x^{2}}{2} = \frac{{(2 \sqrt{5})}^{2}}{2}$ $= 10 sq units$
	Answered by a.lgnaoui last updated on 08/Oct/22

	$BD = DE \Rightarrow (∡ ABC = \frac{π}{4} DEB = \frac{3 π}{4})$ $Posons BD = x EC = y BE = x \sqrt{2}$ ${CD}^{2} = {ED}^{2} + {EC}^{2} - 2 ED \times ECcos 3 \frac{π}{4}$ $100 = x^{2} + y^{2} + \sqrt{2} x y (1)$ $\frac{\sin ∡ CDE}{y} = \frac{\sin 3 \frac{π}{4}}{10} (2)$ $∡ CDE = ∡ DCA \Rightarrow \sin (CDE) = \sin ∡ DCA = \frac{x}{10} (DE ∣∣ AB)$ $(1) \Rightarrow \frac{x}{10 y} = \frac{\sqrt{2}}{20} x = \frac{y \sqrt{2}}{2}$ $(1) \Leftrightarrow 100 = \frac{y^{2}}{2} + y^{2} + y^{2} = \frac{5 y^{2}}{2}$ $y = 2 \sqrt{10} x = 2 \sqrt{5} \sin ∡ C DE = \frac{\sqrt{5}}{5}$ $d o n c a i r e d e l a p a r r i e v e r t e$ $A i r e = 10 \times \frac{EH}{2} = 10 \frac{x \sin ∡ EDC}{2} = 5 \times 2 \sqrt{5} \times \frac{\sqrt{5}}{5}$ $A i r e = 10$
	Commented by a.lgnaoui last updated on 08/Oct/22

	Commented by a.lgnaoui last updated on 08/Oct/22

	$H \in CD \sin (∡ EDH) = \sin (∡ EDC) = \frac{EH}{ED}$
	Commented by Tawa11 last updated on 09/Oct/22

	$Great sirs .$
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