Question

hey friends.................

Here is my question.......

Find out the perimeter of a
rectangle with maximum area
drawn in a circle of diameter 'D'.

Answer 1

maximum area means maximum perimeter
Perimeter of rectangle,
P=2x+2y
theta be angle between diagonal and length
x=length
y=breadth
 

Where:
x=Dcosθ

y=Dsinθ
 

P=2Dcosθ+2Dsinθ

dPdθ=−2Dsinθ+2Dcosθ=0

−sinθ+cosθ=0

sinθ=cosθ

sinθcosθ=1

tanθ=1

θ=45∘
 

x=Dcos45∘=0.707D

y=Dsin45∘=0.707D
 

x=y (square)

Answer 2

if rectangle have maximum area in a circle then its diagonal is diameter of circle and it have length= breadth
so d= √(x^2 +x^2) here x=side of rectangle
x=d/√2
perimeter=4x
so perimeter =4d/√2=2√2d answer