A wire is bent in the shape of a square of side 10cm. If the wire is rebent into rectangle of length 12 cm, find the breadth of a rectangle
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Step-by-step explanation:
Side of the square = 10 cm
Length of the wire = Perimeter of the square
= 4 x side
= 4 x 10cm
= 40 cm
Length of the rectangle, l = 12 cm. Let b be the breadth of the rectangle.
Perimeter of rectangle Length of wire = 40 cm
Perimeter of the rectangle = 2 (l + b)
40 = 2 (12 + b)
(OR) 40 / 2 = 12 + b
b = 20 - 12 = 8 cm
Therefore,The breadth of the rectangle is 8 cm.
Area of the square = (side)²
= 10 cm × 10 cm = 100cm²
Area of the rectangle = l × b
= 12cm × 8cm = 96cm²
So , the square encloses more area even though its perimeter is the same as that of the rectangle.