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Question Number 58876 by mr W last updated on 01/May/19

Commented by math1967 last updated on 01/May/19

$I s i t \frac{1}{3} p a r t s i r ?$
Commented by mr W last updated on 01/May/19

$c o r r e c t s i r!$
Commented by math1967 last updated on 01/May/19

$△ A O B \sim △ E O D ∴ \frac{B O}{D O} = \frac{A B}{D E} = \frac{2}{1}$ $A g a i n \frac{A r △ A O B}{A r △ A O D} = \frac{B O}{D O} = \frac{2}{1}$ $∴ △ A O B : △ D A B = 2 : 3$ $∴ △ A O B = \frac{2}{3} △ D A B = \frac{2}{3} \times \frac{1}{2} A B C D$ $= \frac{1}{3} A B C D$
Commented by math1967 last updated on 01/May/19

	Answered by tanmay last updated on 01/May/19

	$t a n θ = \frac{\frac{a}{2}}{a} = \frac{1}{2}$ $t h e e q o f s t l i n e s w h i c h e n c l o s e t h e s h a d e d a r e a$ $(1) x a x i s (2) \frac{x}{a} + \frac{y}{a} = 1 (3) y = t a n (90 - θ) x$ $y = c o t θ x \to y = 2 x$ $n o w s o l v e y = 2 x a n d x + y = a$ $3 x = a x = \frac{a}{3} a n d y = \frac{2 a}{3}$ $t h e s h a d e d t r i a n g l e s a y A B C$ $p o i n t A (0, 0) B (a, 0) C (\frac{a}{3}, \frac{2 a}{3})$ $a r e a o f △ A B C = \frac{1}{2} \times a \times \frac{2 a}{3} = \frac{a^{2}}{3}$ $a r e a o f s h a d e d t r i a n g l e = \frac{1}{3} (a r e a o f s q u a r e)$
	Commented by tanmay last updated on 01/May/19

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