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Question Number 188095 by normans last updated on 25/Feb/23

Commented by infinityaction last updated on 25/Feb/23

$20$
Commented by Rasheed.Sindhi last updated on 26/Feb/23

$W e l c o m e a f t e r l o n g a b s e n c e$ $i n f i n i t y a c t i o n s i r!$
Commented by infinityaction last updated on 26/Feb/23

$n o s i r m y s e c o n d i d i s u n i v e r s e$
Commented by Rasheed.Sindhi last updated on 26/Feb/23
�� thank you!
	Answered by mr W last updated on 25/Feb/23

	Commented by mr W last updated on 25/Feb/23

	$\tan α = \frac{1}{3}$ $2 β + \frac{π}{2} - 2 α = π$ $\Rightarrow β = \frac{π}{4} + α$ $γ + 2 (\frac{π}{2} - α) = π$ $\Rightarrow γ = 2 α$ $A_{p i n k} = \frac{12 x \times 2 \times 12 x \cos β \times \cos β}{2} = 30$ ${(12 x)}^{2} \cos^{2} β = 30$ ${(12 x)}^{2} {(\cos α - \sin α)}^{2} = 60$ ${(12 x)}^{2} {(\frac{3}{\sqrt{10}} - \frac{1}{\sqrt{10}})}^{2} = 60$ ${(12 x)}^{2} = 150$ $\Rightarrow x^{2} = \frac{150}{144} = \frac{25}{24}$ $A_{b l u e} = \frac{4 x \times 8 x \times \sin γ}{2} = 16 x^{2} \sin (2 α)$ $= 16 \times \frac{25}{24} \times 2 \times \frac{1}{\sqrt{10}} \times \frac{3}{\sqrt{10}}$ $= 10 ✓$
	Commented by manxsol last updated on 26/Feb/23

	$2 α = 45 t g α = \frac{1}{3} α = 18.43 ?$
	Commented by mr W last updated on 26/Feb/23

	$l o o k a t m y c o m m e n t b e l o w!$
	Answered by manxsol last updated on 26/Feb/23

	$\frac{12 x h}{2} = 30 \Rightarrow x h = 5$ $\frac{8 (x h)}{2} = \frac{8 \times 5}{2} = 20$
	Commented by manxsol last updated on 26/Feb/23


	Commented by mr W last updated on 26/Feb/23

	$b e c a r e f u l!$ $t h e d i a g o n a l w h i c h l o o k s l i k e d i a g o n a l$ $a n d y o u t o o k a s d i a g o n a l i s i n f a c t$ $n o t t h e d i a g o n a l!$ $f r o m t h e p r o p o r t i o n o f 4 x a n d 8 x i n$ $t h e d i a g r a m, y o u c a n s e e 8 x i s n o t$ $2 t i m e s a s l o n g a s 4 x, t h a t m e a n s$ $t h e d i a g r a m i s n o t d r a w n t o s c a l e .$ $w h e n y o u d r a w t h e d i a g r a m t o s c a l e,$ $i t s h o u l d l o o k l i k e t h i s :$
	Commented by mr W last updated on 26/Feb/23

	Commented by mr W last updated on 26/Feb/23

	$t h e r e f o r e t h e s o l u t i o n i s n o t a s e a s y$ $a s$ $? = \frac{8 x}{12 x} \times 30 = 20$ $i w a s n o t m i s g u i d e d b y t h e ‘ ‘ {w r o n g}^{″}$ $d i a g r a m, s o i s e l e c t e d a ‘ ‘ {c o m p l i c a t e d}^{″},$ $b u t c o r r e c t w a y t o s o l v e .$
	Commented by manxsol last updated on 26/Feb/23

	Commented by manxsol last updated on 26/Feb/23

	$12 a (2 {c o s}^{2} - 1, - 2 s i n α c o s α)$ $(9.6 a, - 7.2 a)$ $v = (12, 0) - (9.6, 7.2)$ $v = (2.4, 7.2)$ $P = C - v$ $P = (12 a, 12 a) - (2.4, 7.2)$ $P = (9.6 a; 4.8 a)$ $h_{b l u e} = 12 a - 9.6 a = 2.4 a$ $h_{p i n k} = 4.8 a$ $(4.8 a) (12 a) = 60$ $a^{2} = \frac{25}{24}$ $A_{b l u e} = (8 a) (2.4 a) \frac{1}{2}$ $A_{b l u e} = (\frac{48}{5}) (\frac{25}{24}) = 10$ $Y o u a r e g r e a t a n d g e n e r o u s .$ $M u c h a s g r a c i a s$
	Commented by manxsol last updated on 26/Feb/23

	$a l l u n d e r s t o o d . i s a c l e a r$ $c a s e o f o r i g a m i$
	Commented by manxsol last updated on 26/Feb/23


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