Question

a wire is in the shape of a rectangle is it is length is 40 cm and breadth is 22 CM if the same wire is bent in the shape of a square what will be the measure of each side also find which shape enclose more area​

Answer 1

Step-by-step explanation:

Given:-

A wire is in the shape of a rectangle is it is length is 40 cm and breadth is 22 CM if the same wire is bent in the shape of a square.

To find:-

what will be the measure of each side also find which shape enclose more area ?

Solution:-

Length of the rectangular shaped wire = 40 cm

Breadth of the rectangular shaped wire = 22 cm

Total length of the rectangular wire =Perimeter of the rectangle

=>2(length + breadth) units

=>2(40+22) cm

=>2(62) cm

=>124 cm

Perimeter of the wire = 124 cm

If it is bent to the square shaped wire then

Total length of the rectangular wire = Total length

of the square shaped wire

=>4× Length of square side = 124

=>Length of the side of the square = 124/4

=>Length of the side = 31 cm

Now Area of the rectangle = length × breadth

=>40×22 sq.cm

=>880 sq.cm

Area of the rectangular shaped wire = 880 sq.cm

Area of the square shaped wire =

Side × Side sq.units

=>31×31 sq.cm

=>961 sq.cm

Area of the square shaped wire = 961 sq.cm

961 sq.cm > 880 sq.cm

Ar(square ) > Ar(rectangle)

Answer:-

Each side of the square shaped wire = 31 cm

Area of the rectangular shaped wire = 880 sq.cm

Area of the square shaped wire = 961 sq.cm

Square shaped wire occupies more area than that of the rectangular shaped wire

Used Concept:-

• If a rectangular figure is bent to a square shaped figure the total lengths of both figures are remains same.

Used formulae:-

• Perimeter of a square = 4×length of the side
• Perimeter of a rectangle =

2(length +breadth)

• Area of a square = side ×side
• Area of a rectangle = length× breadth