Question

he perimeter of a rectangle is 108cm. If the length is 6cm more than twice the breadth, find the length and breadth of the rectangle.

Answer 1

Given :-

• The perimeter of a rectangle is 108cm.  

• The length is 6cm more than twice the breadth.  

To Find :-

• Find the length and breadth of the rectangle.

Solution :-

~Here, we’re given that perimeter of a rectangle is 108 cm, the length is 6cm more than twice the breadth and we need to find the length and breadth of the rectangle. Firstly, we’ll assume the breadth and length accordingly and after putting the values in the formula of perimeter we can find the required answer.  

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As we know that,

★ Perimeter of rectangle = 2( l + b )

Where,  

• l is length  
• b is breadth  

→  Let the breadth be ‘ x ’  

→ Then the length will be ‘ 2x + 6 ’  

[ According to the question ]  

Finding value of x :-

➟ 2( x + 2x + 6 ) = 108 cm  

➟ 2( 3x + 6 ) = 108 cm  

➟ 3x + 6 = 108/2  

➟ 3x + 6 = 54

➟ 3x = 54 – 6  

➟ 3x = 48  

➟ x = 48/3  

➟ x = 16  

Finding length and breadth :-

• Length = 2x + 6 = 2( 16 ) + 6 = 32 + 6 = 38 cm
• Breadth = x = 16 cm

Hence,  

• Length and breadth of rectangle are 38 cm and 16 cm

Verification :-

➟ 2( 16 cm + 38 cm ) = 108 cm  

➟ 2( 54 cm ) = 108 cm  

➟ 108 cm = 108 cm

• LHS = RHS

Hence, verified ✓

Answer 2

QuestioN :

The perimeter of a rectangle is 108cm. If the length is 6cm more than twice the breadth, find the length and breadth of the rectangle.

GiveN :

• Length of the Rectangle = 6 less than twice its breadth  
• Perimeter of the Rectangle = 54

To FiNd :

• Length and Breadth of the Rectangle

ANswer :

The Length is 16 units and the Breadth is 11 units.

SolutioN :

Let the Breadth be x,

Let the Length be as (2x - 6).

By using the formula,

Perimeter = 2 ( length + Breadth )

Let's find the breadth,

$\sf \implies 2(2x-6+x)=54$

$\sf \implies 2x-6+x=54$ ÷ $\sf 2$

$\sf \implies 3x-6=33$

$\sf \implies 3x = 27+6$

$\sf \implies 3x=33$

$\sf \implies x= \dfrac{33}{3}$

$\sf \implies x = 11$

Breadth = 11 units

Let's find the length,

$\sf \implies 2x-6$

$\sf \implies2(11)-6$

$\sf \implies 22-6$

$\sf \implies 16$

Length = 16 units

∴Hence, The Length is 16 units and the Breadth is 11 units.

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