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Question : 68 of 160
Marks:
+1,
-0
Solution:
Let
â–³ABC is a right angled triangle with base
BC(x), perpendicular or height
AB(y) and hypotenuse
AC(h).
‌‌ Area ‌=‌×xy‌⇒‌‌A2=‌x2y2‌⇒‌‌A2=‌x2[h2−x2] [
∵ using Pythagoras theorem]
‌⇒‌‌A2=‌[h2x2−x4]‌⇒‌‌‌=‌[2h2x−4x3] 
[A′=A2] ‌⇒‌‌‌=0‌⇒‌‌x≠0So,
x2=‌ or
x=‌⇒‌=‌[2h2−12x2] ⇒‌|x=‌=‌[2h2−12×‌]<0 A is maximum at
x=‌‌y2=h2−x2‌=h2−‌=‌‌⇒‌‌y=‌ Area of
∆ABC‌=‌×x×y‌=‌×‌×‌=‌
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