Question

18. 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.
​

Answer 1

Answer:

see the above pic it will help you

Answer 2

Given :-

• The perimeter of a rectangle is 108cm.  
• The length is 6cm more than twice the breadth.  

To Find :-

• The length and breadth of the rectangle.

Solution :-

•  Let the breadth be ‘ x ’  

$\qquad$☀It's given that, the length is 6cm more than twice the breadth and the perimeter of a rectangle is 108cm.  

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

Formula used :-

• Perimeter of rectangle = 2( l + b )

Where:-

• l = length  
• b = breadth  

$\qquad\small\underline{\pmb{\sf \:According \: to \: the \: question :-}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ 2( x + 2x + 6 ) = 108 cm  }}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 2( 3x + 6 ) = 108 cm  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 3x + 6 = \dfrac{108}{2}}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 3x + 6 = 54}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 3x = 54 – 6  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 3x = 48  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x =\cancel{\dfrac{48}{3} }}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ x = 16  }}}$

$\qquad$ ⎘ Finding length and breadth :-

$\qquad$☀ Length = 2x + 6= 32 + 6 = 38 cm

$\qquad$☀ Breadth = x = 16 cm

Verification :-

$\qquad$ ⎘ It's given that the perimeter of a rectangle is 108cm.  

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ 2( 16 cm + 38 cm ) = 108 cm}}}$  

$\qquad\leadsto\quad \pmb {\mathfrak{ 2( 54 cm ) = 108 cm  }}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ 108 cm = 108 cm }}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ LHS = RHS }}$

• Hence, verified..!

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