Question-47010

Question Number 47010 by ajfour last updated on 03/Nov/18

Commented by ajfour last updated on 03/Nov/18

F i n d m a x i m u m r e c t a n g u l a r

a r e a a n d l & h (t h e n), i n t e r m s

o f s i d e s a, b, c o f △ A B C .

(w i t h Q R a l o n g B C)

Answered by ajfour last updated on 04/Nov/18

a r e a (△ A B C) = △_{0}

\frac{A r (△ A P S)}{△_{0}} = {(\frac{l}{a})}^{2}

\frac{A r (△ P B Q) + A r (△ S R C)}{△_{9}} = {(\frac{a - l}{a})}^{2}

\Rightarrow l h = △_{0} [1 - {(\frac{l}{a})}^{2} - {(1 - \frac{l}{a})}^{2}]

= 2 △_{0} (\frac{l}{a}) (1 - \frac{l}{a})

\Rightarrow m a x (l h) w h e n \frac{l}{a} = \frac{1}{2}

m a x (P Q R S) = \frac{△_{0}}{2}, l = \frac{a}{2}

h = \frac{a l t i t u d e o f △ A B C}{2} .

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