Question

a wire is bent in the shape of rectangle whose breath is 24 cm is rebent in the shape of square of side 28 cm Find the length of rectangle and which shape encloses more area​

Answer 1

Answer:

Length is 32cm

Area of square is 784 cm sq

Area of rectangle is 768 cm sq

Hence square had higher area

Step-by-step explanation:

Perimeter of square is 4×28=112 cm

Since the same wire is used to make the rectangle, the perimeter is same. Hence

$2 \times (l + b) = 112$

$2(24 + l) = 112$

$(24 + l)= 56$

$l= 32$

Answer 2

DIAGRAM:

Rectangle:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\multiput(1,0)(0,2){2}{\line(1,0){3.2}}\multiput(1,0)(3.2,0){2}{\line(0,1){2}}\multiput(-0.2,1)(4.5,0){2}{ \bf 24 \ cm }\multiput(2,-0.3)(0,2.4){2}{ \bf x \ cm }\put(0.7,-0.25){ \bf E }\put(0.7,2){ \bf F }\put(4.25,-0.25){ \bf H }\put(4.3,2){ \bf G }\end{picture}$

Square:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\multiput(1,0)(0,2.4){2}{\line(1,0){2.4}}\multiput(1,0)(2.4,0){2}{\line(0,1){2.4}}\multiput(-0.2,1)(3.7,0){2}{ \bf 28 \ cm }\multiput(1.5,-0.3)(0,2.8){2}{ \bf 28 \ cm }\put(0.7,-0.25){ \bf A }\put(0.7,2.4){ \bf B }\put(3.5,-0.25){ \bf D }\put(3.5,2.4){ \bf C }\end{picture}$

ANSWER:

• The length of rectangle = 32 cm.

• The shape which encloses more area​ is square.

GIVEN:

• A wire is bent in the shape of rectangle whose breath is 24 cm.

• It is again bent in the shape of square of side 28 cm.

TO FIND:

• The length of rectangle.

• The shape which encloses more area​.

EXPLANATION:

Let the length of the rectangle be x.

As the length of the wire is same perimeter of the square and rectangle will be the same.

Perimeter of square = 4a units.

Perimeter of rectangle = 2(l + b) units.

Perimeter of square = Perimeter of rectangle

4a = 2(l + b)

2a = l + b

a = 28 cm

l = x cm

b = 24 cm

2(28) = 24 + x

58 = 24 + x

x = 32 cm

Length of the rectangle = 32 cm

Area of square = a² sq. units

a = 28 cm

Area of square = 28²

Area of square = 784 cm²

Area of rectangle = l × b sq. units.

l = 32 cm

b = 24 cm

Area of rectangle = 32 × 24

Area of rectangle = 768 cm²

Hence square has the more area than rectangle.