Question

A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of
length 12 cm, find its breadth. Which encloses more area - the square or the
rectangle?​

Answer 1

Step-by-step explanation:

The length of wire remains same, so when in square form it's length is 4*10 = 40 cm

It's area is 10*10 = 100cm²

When bent into rectangle, length is 12, using P = 2(l+b) formula:

2(12+b) = 40 as the length remains same

12+b = 20

b = 8

Area is 12 * 8 = 96 cm²

So square encloses more area

Answer 2

Answer :

• Area of square encloses more area so, area of square is greater than area of rectangle
• Breadth =8cm

Given :

• A wire is in the shape of a square of side 10cm
• The wire is rebent into rectangle of length 12cm

To find :

• Breadth
• which encloses more area , the square or rectangle

Solution :

when we converting the square wire into rectangle then we get length of wire it will be same so ,

• Perimeter of square = Perimeter of rectangle

As we know that,

• Perimeter of square = 4a
• Perimeter of rectangle = 2(l + b)

(1) Perimeter of square :

Given,

• Side of square is 10cm

As we know that ,

• Perimeter of square = 4a

where a is 10cm

》4(10)

》40cm

(2) Perimeter of rectangle :

Given that,

• Length = 12cm
• Breadth = ?

As we know that,

• Perimeter of rectangle = 2(l + b)

where, l is length 12cm and b is breadth

》2(l + b)

》2(12 + b)

》12cm

Then,

Now we need to find breadth

• Perimeter of square = Perimeter of rectangle

》40 = 2(12 + b)

》40/2 = 12 + b

》20 = 12 + b

》b = 20 - 12

》b = 8 cm

Hence , Breadth of rectangle is 8cm

Now we need to find the enclose more area , square or the rectangle

(1) Square:

As we know that,

• Area of square = a²

where a is 10

》10²

》100 cm²

(2) Rectangle :

As we know that,

• Area of rectangle = l × b

where , l is length 12cm and b is breadth 8cm

》12 × 8

》96cm²

Hence , Area of square encloses more area so, area of square is greater than area of rectangle