Q. 94.7( 3 Votes )
Given the sum of the perimeters of a square and a circle, show that the sum of their areas is least when one side of the square is equal to diameter of the circle.
Answer :
Let us say the sum of perimeter of square and circumference of circle be L
Given: Sum of the perimeters of a square and a circle.
Assuming, side of square = a and radius of circle = r
Then, L = 4a + 2πr …1
Let the sum of area of square and circle be S
So, S = a2 + πr2
S = 
Condition for maxima and minima
= 0
So, for 
>0
This is the condition for minima
From equation 1
Substituting from equation 2
a = 2r
Hence, proved.
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PREVIOUSA wire of length 20 m is to be cut into two pieces. One of the pieces will be bent into shape of a square and the other into shape of an equilateral triangle. Where the wire should be cut so that the sum of the areas of the square and triangle is minimum?NEXTFind the largest possible area of a right angled triangle whose hypotenuse is 5 cm long.
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