Question

A wire is in the shape of a rectangle. it's length is 40 cm and breadth is 22 cm. if the same wire is rebent in the shape of a square and then into a circle, find :a) side of square b) radius of circle

Answer 1

The most important thing that stays unchanged is the length of the wire which is the perimeter of all the diagrams or objects
Perim of the Rectangle is
2( l+b) = 2( 40 + 22) = 2*62= 124 cm
length of the wire is 124 cm ,
let there be a square made of it and let it's sides be x
then it's perim would be 4x
so 4x = 124
x = 31 cm is the side of the square
Let there be a circle of radius x
then it's perimeter would be 2pi* x
then 2 * pi * x = 124
x = 62/pi

Answer 2

length of the wire=Perimeter of rectangle
=2(l+b)
=2(40+22)
=2×62
=124 cm
Same wire is rebent into square
=> perimeter of square=length of the wire
4×side=124
$side = \frac{124}{4}$
side=31 cm
=> Side of the square is 31 cm

Note the wire is rebent into circle
=>circumference of the circle=length of the wire
2πr=124
$2 \times \frac{22}{7} \times r =124 \\ r = \frac{124 \times 7}{2 \times 22} = 19.7(approx)$
radius of the circle is 19.7 cm