Question

The wire is in the shape of a rectangle. It's length is 32 cm and breadth is 18 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

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Answer 1

Answer:

Square has more area than the area of rectangle

The length of each side of the square=25cm

Step-by-step explanation:

Given:-

The wire is in the shape of a rectangle. It's

length is 32 cm and breadth is 18 cm. If the same wire is rebent in the shape, of a square, what will be the measure of each side?

To find:-

Find which shape encloses more area.

Using Concept:-

If the planar figure is converted into another planar figure then the perimeter is same

Using formula:-

Perimeter of a rectangle whose length and breadth are "l" and"b" units is 2(l+b) units

Perimeter of a square whose side is "a" units is 4a units.

Area of a rectangle=lb square units

Area of a rectangle=lb square unitsArea of a square=a² sq.units

Solution:-

The given wire is in the shape of rectangle

The length of the rectangle(l)=32 cm

The breadth of the rectangle(b)=18cm

Perimeter of the rectangleP)=2(l+b) units

=>P=2(32+18)

=>P=2(50)

=>P=100 cm

If it is converted into square then the total length of the wire does not change.

Perimeter of the rectangle=Perimeter of the square

=>4a=100cm

=>a=100/4cm

=>a=25cm

Side of the square=25 cm

The area of the rectangle=l×b

=>32×18

=>Area=576 sq.cm-----(1)

Area of the square =a²

=>25²

=>25×25

=>625sq.cm-----(2)

625sq.cm>576sq.cm

Square has more area than the area of rectangle

Answer:-

Square has more area than the area of rectangle.

The length of each side of the square=25cm

Answer 2

Given :

• Length of rectangle = 32 cm
• Breadth of rectangle = 18 cm

To find :

• Area of rectangle
• Area of square

According to the question,

➞ Perimeter of square = Perimeter of rectangle

➞ 4 × Side = 2( length + breath)

[ Note :- Let the side be a ]

➞ 4a = 2(32 + 18) cm

➞ 4a = 2(50cm)

➞ 4a = 100 cm

➞ a = 100 ÷ 4 cm

➞ a = 25 cm

So,the side of a square is 25 cm.

Now,

➞ Area of rectangle = Length × Breadth

➞ Area of rectangle = 32 cm × 18 cm

➞ Area of rectangle = 576 cm²

So,the area of rectangle is 576 cm².

➞ Area of square = Side × Side

➞ Area of square = 25 cm × 25 cm

➞ Area of square = 625 cm²

So,the area of square is 625 cm².

.°. The square shape encloses more area of 625 cm².