Question

A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 13 cm, find its breadth. Which shape encloses more area?​

Answer 1

Answer:

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=100cm

2

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

=4cm

2

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

2

.

Step-by-step explanation:

i hope u understand dear

Answer 2

Answer:-

Let a be the side of a square, l be the length and b be the breadth of rectangle.

$\sf \: side \: of \: the \: square = 10 \: cm$

$\sf \: Perimeter =10×4=40 \: cm$

Length of the rectangle = 13 cm

Breadth of the rectangle = b

Perimeter of square = perimeter of rectangle = 40 cm

As length of wire is constant, perimeter of both shapes would be same,

$\sf \longrightarrow \: 4a=2(l+b)$

$\sf \longrightarrow 40=2(13+b)$

$\sf \longrightarrow \cancel\frac{40}{2} = 13 + b$

$\sf \longrightarrow 20 = 13 + b$

$\sf \longrightarrow \: b = 20 - 13$

$\sf \longrightarrow \: b = 7 \: cm$

$\sf \: Area \: of \: square=a²$

$\sf \longrightarrow \: 10²$

$\sf \longrightarrow 100 \: {cm}^{2}$

$\sf \: Area \: of \: rectangle=l×b$

$\sf \longrightarrow \: 13 \times 7$

$\sf \longrightarrow 91 \: {cm}^{2}$

Area of square is greater.