Q. 7

# A wire of length

Let the length of side of square be a and radius of circle be r.

It is given that wire is cut into two parts to form a square and a circle

Therefore, perimeter of square + circumference of circle = length of wire 4a + 2πr = 28 a = …1

Let us assume area of square + area of circle = S S = a2 + πr2 S = + πr2 (from equation 1)

Condition for maxima and minima      …2 So, for   >0

This is the condition for minima

From equation 1

a = Substituting from equation 2 a =  a =  a =  Hence, radius of circle and length of square be and respectively.

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