Q.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?

Given: Length = 40 cm,
Breadth = 22 cm
Perimeter of the rectangle= Length of the wire
= 2(l + b) = 2(40 cm + 22 cm)
= 2 × 62 cm = 124 cm
Now, the wire is rebent into a square.
Perimeter = 124 cm
Or, 4 × side = 124
\(\therefore \)side = \(\frac{124}{4} \) cm = 31 cm
So, the measure of each side = 31 cm
Area of rectangular shape = l × b
= 40 cm x 22 cm = 880\( cm^2\)
Area of square shape = Side× side
= \( (31)^2 = 961 cm^2 \)
Since 961\( cm^2 > 880 cm^2 \)
Hence, the square encloses more area.