(23
(12) A wire of length 36 meters is bent in the form
of a rectangle. Find its dimensions if the area
of the rectangle is maximum.
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Given
Case I : A wire is bent in shape of rectangle.
length=36 cm
Breath=25 cm
Total length of wire is = Perimeter of rectangle
=2(l+b)
=2[36+25]
⇒2(61)=122 cm
length of wire =122 cm
Area occupied by wire =l×b=36×25
⇒AR=900 cm2
Case II: If this wire is bent in shape of square then,
length of wire = Perimeter of square
122=4a
a=4122=261cm
Now area of wire is shape of square =a2
As=(261)2=930.25 cm2
Hence the wire is bent in shape of square then it has each side of 30.5 cm each
And square shape occupies more area.
As=930.25 cm2
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