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Question Number 187968 by normans last updated on 24/Feb/23

Commented by a.lgnaoui last updated on 24/Feb/23

$21 ?$
Commented by a.lgnaoui last updated on 24/Feb/23

$I t h i n k i n t o p = 21 = m e s u r e o f l i n e$ $a n d d o w n = (A r e a)$
Commented by a.lgnaoui last updated on 24/Feb/23

$o r t h e i n v e r s e$
Commented by normans last updated on 25/Feb/23

$n o s i r$
Commented by mr W last updated on 25/Feb/23

$w r o n g!$ $e v e n b l i n d p e o p l e c a n c l e a r l y s e e t h a t$ $b l u e a r e a m u s t b e m u c h b i g g e r t h a n$ $t h e g r a y a r e a 21 . s o 21 i s c l e a r l y w r o n g .$ $100 i s t h e r i g h t a n s w e r .$
	Answered by mr W last updated on 25/Feb/23

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

	$\frac{d + c}{d} = \frac{28}{a} \Rightarrow \frac{c}{d} = \frac{28}{a} - 1 . . . (i)$ $\frac{d + c}{c} = \frac{2 b}{a} \Rightarrow \frac{d}{c} = \frac{2 b}{a} - 1 . . . (i i)$ $(i) \times (i i) :$ $1 = (\frac{28}{a} - 1) (\frac{2 b}{a} - 1)$ $\Rightarrow 14 (2 b - a) = a b . . . (I)$ $\frac{d + e}{d} = \frac{21}{b} \Rightarrow \frac{e}{d} = \frac{21}{b} - 1 . . . (i i i)$ $\frac{d + e}{e} = \frac{a}{b} \Rightarrow \frac{d}{e} = \frac{a}{b} - 1 . . . (i v)$ $(i i i) \times (i v) :$ $1 = (\frac{21}{b} - 1) (\frac{a}{b} - 1)$ $\Rightarrow 21 (a - b) = a b . . . (I I)$ $14 (2 b - a) = 21 (a - b)$ $\Rightarrow \frac{b}{a} = \frac{5}{7}$ $21 (\frac{a}{b} - 1) = a$ $\Rightarrow a = 21 (\frac{7}{5} - 1) = \frac{42}{5}$ $\Rightarrow \frac{d + c}{d} = \frac{28}{a} = \frac{28 \times 5}{42} = \frac{10}{3}$ $A_{b l u e} = \frac{2 b (d + c)}{2}$ $A_{g r a y} = \frac{a d}{2} (= 21)$ $\frac{A_{b l u e}}{A_{g r a y}} = \frac{2 b}{a} \times \frac{d + c}{d} = \frac{2 \times 5}{7} \times \frac{10}{3} = \frac{100}{21}$ $A_{b l u e} = \frac{100}{21} A_{g r a y} = \frac{100}{21} \times 21 = 100 ✓$
	Commented by normans last updated on 25/Feb/23

	$y e s, t h i s i s t h e r i g h t s o l u t i o n I m e a n .$ $T h a n k s P r o f . .$
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