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Question Number 78937 by mr W last updated on 21/Jan/20

Commented by mr W last updated on 21/Jan/20

$A s s h o w n, t h e a r e a s o f t h r e e p a r t s o f$ $a r e c t a n g l e a r e g i v e n . F i n d t h e a r e a$ $o f t h e f o u r t h p a r t .$
Commented by john santu last updated on 22/Jan/20

$t h e A r e a i s r e q u i r e d =$ $\sqrt{{(A + B + C)}^{2} - 4 A C}$
Commented by john santu last updated on 22/Jan/20

$t h a t r i g h t s i r ?$
Commented by mr W last updated on 22/Jan/20

$n o s i r!$ $c o r r e c t r e s u l t s e e s o l u t i o n b e l o w f r o m$ $a j f o u r s i r . i t i s \sqrt{{(A + B + C)}^{2} - 4 A B} .$
Commented by john santu last updated on 22/Jan/20

$o o y e s . i^{'} m w r o n g t o c a l c u l a t e$
	Answered by ajfour last updated on 21/Jan/20

	$l e t r e c t a n g l e l e n g t h = a + c$ $h e i g h t = b + d$ $2 B = (a + c) b$ $2 A = (b + d) a$ $2 C = c d$ $l e t ? = Q$ $Q = (a + c) (b + d) - (A + B + C)$ $= \frac{4 A B}{a b} - (A + B + C)$ $(2 B - a b) (2 A - a b) = 2 C a b$ ${(a b)}^{2} - 2 (A + B + C) (a b) + 4 A B = 0$ $a b = (A + B + C) - \sqrt{{(A + B + C)}^{2} - 4 A B}$ $h e n c e$ $Q = \frac{4 A B}{(A + B + C) - \sqrt{{(A + B + C)}^{2} - 4 A B}} - (A + B + C)$
	Commented by mr W last updated on 22/Jan/20

	$t h a n k y o u s i r! p e r f e c t!$ $t h e l a s t l i n e c a n b e s i m p l i f i e d t o$ $Q = \sqrt{{(A + B + C)}^{2} - 4 A B}$
	Commented by mr W last updated on 22/Jan/20

	$+ s i g n i s s u i t a b l e, s i n c e a b > A + B + C$ $a b = (A + B + C) + \sqrt{{(A + B + C)}^{2} - 4 A B}$
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