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Question Number 121802 by prakash jain last updated on 11/Nov/20

Commented by prakash jain last updated on 11/Nov/20

$ajfour sir, i cannot find the original$ $question but i got x \notin R .$ $Please check . I will also recheck .$ $Thanks .$
Commented by ajfour last updated on 11/Nov/20

$I d o n t k n o w w h a t t o s a y, P r a k a s h S i r,$ $u n d e r s t a n d i n g t h a t t h e q u e s t i o n$ $i s f a u l t y, i d e l e t e d i t .$ $Y o u r m e t h o d s u g g e s t s m e t o a m e n d$ $t h e q u e s t i o n t h i s w a y . . .$ $C o n s i d e r o n l y E a b o v e g r o u n d,$ $s u c h t h a t t h e p i n k, y e l l o w, b l u e,$ $a n d g r e e n a r e a s a r e t r i a n g u l a r$ $f a c e s o f a t e n t, w h i l e △ B C F$ $a l o n g g r o u n d, a n d i f e a c h o f$ $t h e s e a r e a s a r e e q u a l, f i n d$ $(x_{E}, y_{E}, z_{E}) t a k i n g A (0, 0, 0)$ $a n d + x a l o n g A D, + y a l o n g A B .$ $+ z v e r t i c a l l y u p w a r d s t h r o u g h A .$
	Answered by Olaf last updated on 11/Nov/20

	$All colored regions have equal$ $area \frac{AB \times AD}{5} = \frac{a}{5}$ $If A (0, 0) is the origin, E (x, y) and F (z, 0) :$ $- pink area = \frac{1}{2} (1 \times x) = \frac{a}{5}$ $\Rightarrow x = \frac{2}{5} a$ $- blue area = \frac{1}{2} (a \times (1 - y)) = \frac{a}{5}$ $\Rightarrow y = \frac{3}{5}$ $- yellow area = \frac{1}{2} (z \times x) = \frac{a}{5}$ $\Rightarrow z = 1$ $- brown area = \frac{1}{2} ((a - 1) \times 1) = \frac{a}{5}$ $\Rightarrow a = \frac{5}{3}$ $AB / AD = a = \frac{5}{3}$
	Commented by prakash jain last updated on 12/Nov/20

	$E = (x, y)$ $Please check .$ $Yellow area = \frac{1}{2} z \times y ?$ $\frac{1}{2} z \times \frac{3}{5} = \frac{a}{5} \Rightarrow z = \frac{2 a}{3}$ $brown area \frac{1}{2} \times (1 - \frac{2 a}{3}) = \frac{a}{6} \neq \frac{a}{5}$
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