# Ex 6.5,19

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.5,19 Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area. Let radius be r of the circle & let be the length & be the breadth of the rectangle Now, ABC is right angle triangle (AB)2 + (BC)2 = (AC)2 2 + 2 = 2 2 2 + 2 = 4 2 2 = 4 2 2 = 4 2 2 We need to maximize Area of rectangle Let A be the area rectangle Area of rectangle = Length Breadth A = xy A = 4 2 2 Diff. w.r.t = 4 4 2 2 = . 4 2 2 + 4 2 2 . = 1 . 4 2 2 + 1 2 4 2 2 . 4 2 2 . = 4 2 2 2 2 2 4 2 2 = 2 4 2 2 2 2 2 2 4 2 2 = 2 4 2 2 2 2 2 4 2 2 = 4 2 2 2 4 2 2 = 4 2 2 2 4 2 2 = 2 2 2 2 4 2 2 Putting = 0 4 2 2 2 4 2 2 =0 2 2 2 = 0 4 2 2 4 2 2 2 = 0 2 = 2 2 2 = 2 2 = 2 2 = 2 Finding 2 2 = 2 2 2 2 4 2 2 Diff w.r.t 2 2 = 2 . 2 2 2 4 2 2 2 2 = 2 2 2 2 . 4 2 2 4 2 2 . 2 2 2 4 2 2 2 2 2 = 8 0 2 4 2 2 1 2 4 2 2 . 4 2 2 . 2 2 2 4 2 2 2 2 2 = 8 2 4 2 2 1 2 4 2 2 . 0 2 . 2 2 2 4 2 2 2 2 2 = 8 2 4 2 2 + 2 2 2 4 2 2 4 2 2 2 2 2 = 8 2 4 2 2 2 + 2 2 2 4 2 2 2 4 2 2 2 2 = 8 2 4 2 2 + 2 2 2 4 2 2 1+ 1 2 2 2 = 8 2 4 2 2 + 2 2 2 4 2 2 3 2 Putting = 2 2 2 2 = 2 2 = 8 2 2 4 2 2 2 + 2 2 2 2 2 4 2 2 2 3 2 = 8 2 2 2 r 2 + 2 0 2 2 3 2 = 8 2 2 2 r 2 +0 2 r 2 3 2 = 8 4 2 2 2 2 3 = 16 = 16 < 0 Hence 2 2 < 0 at = 2 Thus area is maximum when = 2 Now, finding y = 4 2 2 Putting 2 = 2 = 4 2 2 2 = 4 2 2 2 = 2 2 = 2 Therefore = = 2 Hence area is maximum when = The rectangle is a square.

Ex 6.5,1
Important

Ex 6.5,2

Ex 6.5,3

Ex 6.5,4

Ex 6.5,5 Important

Ex 6.5,6

Ex 6.5,7 Important

Ex 6.5,8

Ex 6.5,9

Ex 6.5,10

Ex 6.5,11 Important

Ex 6.5,12

Ex 6.5,13

Ex 6.5,14

Ex 6.5,15

Ex 6.5,16

Ex 6.5,17

Ex 6.5,18 Important

Ex 6.5,19 You are here

Ex 6.5,20 Important

Ex 6.5,21

Ex 6.5,22

Ex 6.5,23 Important

Ex 6.5,24

Ex 6.5,25

Ex 6.5,26 Important

Ex 6.5,27

Ex 6.5,28 Important

Ex 6.5,29

Chapter 6 Class 12 Application of Derivatives

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.