Question

22 A wire is in the shape of a square of side 10 cm. While Ram trying to rebend
the same wire into a rectangle 2 cm wire got removed, so, Ram rebent the
remaining wire 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:

Answer:

The square encloses more area by 4 cm^24cm

2

.

To find:

Which figure encloses more area and by how much more they enclosed the area compared to the another figure.

Solution:

Given, Side of the square: 10 cm

Hence, Perimeter of the square = 4 X 10 = 40 cm = Length of the wire.

When wire is re-bend to make a rectangle,

Given, Length of the rectangle= 12 cm

Let the breadth of the rectangle be b

Thus, the perimeter of both the rectangle and the square is same since the square is stretched to make a rectangle.

We know that the Perimeter of rectangle

$\begin{gathered}\begin{array} { c } { = 2 ( l + b ) = 2 ( 12 + b ) } \\\\ { 40 = 24 + 2 b } \\\\ { 2 b = 40 - 24 \Rightarrow 2 b = 16 } \\\\ { b = 8 \mathrm { cm } } \end{array}\end{gathered}$

=2(l+b)=2(12+b)

40=24+2b

2b=40−24⇒2b=16

b=8cm

Area of enclosed by the square

= $( \text {side} ) ^ { 2 } = 10 \times 10 = 100 \mathrm { cm } ^ { 2 }=(side)$

2 =10×10=100cm2

Area enclosed by the rectangle

= $( \text {length} ) \times ( \text {breadth} ) = 12 \times 8 = 96 \mathrm { cm } ^ { 2 }=(length)×(breadth)=12×8=96cm$

2

Thus, Difference in their area

= ( 100 - 96 ) c m ^ { 2 } = 4 c m $^ { 2 }=(100−96)cm$

2 =4cm2

Hence, the square encloses more area by 4 cm^24cm2

.

Answer 2

Answer:

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Step-by-step explanation:

Side of the square = 10 cm

Length of the wire = Perimeter of the square

= 4 x side

= 4 x 10cm

= 40 cm

Length of the rectangle, l = 12 cm. Let b be the breadth of the rectangle.

Perimeter of rectangle Length of wire = 40 cm

Perimeter of the rectangle = 2 (l + b)

40 = 2 (12 + b)

(OR) 40 / 2 = 12 + b

b = 20 - 12 = 8 cm

Therefore,The breadth of the rectangle is 8 cm.

Area of the square = (side)²

= 10 cm × 10 cm = 100cm²

Area of the rectangle = l × b

= 12cm × 8cm = 96cm²

So , the square encloses more area even though its perimeter is the same as that of the rectangle.