Ex 11.1, 6 A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?
We convert
rectangular wire to square
So, length of wire will be the same
∴ Perimeter of rectangle = Perimeter of square
Rectangle
Length of rectangle = l = 40 cm
Breadth of rectangle = b = 22 cm
Perimeter = 2 (l + b)
= 2 (40 + 22)
= 124 cm
Square
Let side = a
Perimeter = 4a
Now,
Perimeter of rectangle = Perimeter of square
124 = 4a
124/4 = a
31 = a
a = 31 cm
So, Side of square is 31 cm
Now,
We need to find whose area is bigger
Finding area
Rectangle
Area = l × b
= 40 × 22
= 88 cm2
Square
Area = a × a
= 31 × 31
= 961 cm2
So,
Area of square is greater then area of rectangle

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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