Question

13. If the perimeter of a rectangle is 10 em and the
difference between its length and breadth is 1 cm.
then in length is
and its breadth​

Answer 1

Answer :-

• The length and breadth of rectangle are 3cm and 2cm respectively.

Step-by-step explanation :

To Find :-

• The length of the rectangle
• The breadth of rectangle

Solution :-

Given that,

• The perimeter of rectangle = 10cm.
• The difference between the length and breadth = 1cm.

Assumption: Let us assume the breadth and length as x and ( x + 1 ) respectively,

As we know that,

Perimeter of rectangle = 2 ( l + b )

Where,

• l = Length
• b = Breadth

=> 2 ( length + Breadth ) = Perimeter

=> 2 ( x + 1 + x ) = 10

=> x + 1 + x = 10/2

=> x + x + 1 = 5

=> 2x + 1 = 5

=> 2x = 5 - 1

=> 2x = 4

=> x = 4/2

=> x = 2

• The value of x is 2.

Now, the length and breadth of rectangle is,

• Length, [ We assumed length as ( x + 1 )

=> ( x + 1 ) cm

=> ( 2 + 1 ) cm

=> 3cm

• Breadth, [ We assumed breadth as x

=> x

=> 2cm.

Hence,

The length and breadth of rectangle are 3cm and 2 cm respectively.

Answer 2

$\underline{~~~~~~~~~~~~~~~~~ \pink{\bf{ \dag{}}} \purple{\frak{Required ~Solution ~~~~~~~~~~~~~~~~~}}}$

Given:

• Perimeter of rectangle = 10 cm

• Difference between learning and breadth = 1cm

To find:

• Length

• Breadth

Let:

• Breadth = x

• Length = x + 1

We know:

$\bigstar \boxed{ \rm{Perimeter_{(rectangle)} =2(length + breadth) }}$

By using this formula we can find value of x

$\leadsto \sf{Perimeter_{(rectangle)} =2(length + breadth)}$

$\leadsto \sf{10=2 \{(x +1 ) + (x) \}}$

$\leadsto \sf{10=2 \{x +1 + x \}}$

$\leadsto \sf{10=2 \{2x +1\}}$

$\leadsto \sf{10=2 \{2x \} +2 \{1\}}$

$\leadsto \sf{10=4x +2}$

$\leadsto \sf{10 - 2=4x}$

$\leadsto \sf{8=4x}$

$\leadsto \sf{4x = 8}$

$\leadsto \sf{x = \dfrac{8}{4} }$

$\leadsto \sf{x = \dfrac{4 \times 2}{4} }$

$\leadsto \sf{x = \dfrac{\cancel4 \times 2}{\cancel4} }$

$\leadsto \sf{x = 2 \times 1}$

$\leadsto \underline{ \boxed{\sf{x = 2}}}$

Verification:

$\leadsto \sf{10=2 \{(x +1 ) + (x) \}}$

put value of x in this equation

$\leadsto \sf{10=2 \{(2 +1 ) + (2) \}}$

$\leadsto \sf{10=2 \{(3) + (2) \}}$

$\leadsto \sf{10=2 \{3 \}+2 \{ 2 \}}$

$\leadsto \sf{10=6+4}$

$\leadsto \underline {\boxed{\sf{10=10}} }$

RHS = LHS

Hence verified!

• Breadth = x
• Breadth = 2cm

• Leanth = x + 1
• Length = 2 + 1
• Length = 3 cm