Question-121802

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 \dots

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}