Question

the perimeter of a square is double that of a triangle if perimeter of square is 120 and length and breadth only rectangle are in the ratio 3 ratio 2 find breadth of rectangle

Answer 1

Answer :

• Breadth of rectangle is 12cm

Given :

• The perimeter of a square is double that of a rectangle
• Perimeter of square is 120
• Length and breadth of a rectangle are in the ratio is 3 : 2

To find :

• Breadth of rectangle

Solution :

• Let the length be 3x
• Let the breadth be 2x

Given that , The perimeter of a square is double that of a rectangle then

• Perimeter of square = 2 × perimeter of rectangle

Perimeter of square is 120

》120 = 2[2(l + b)]

》120 = 2[2(3x + 2x)]

》2(3x + 2x)= 120/2

》 2(3x + 2x) = 60

》 2(5x) = 60

》 5x = 60/2

》5x = 30

》x = 30/5

》 x = 6

or

》120 = 2[2(3x + 2x)]

》 2(3x + 2x)= 120/2

》 2(3x + 2x) = 60

》2(5x) = 60

》10x = 60

》x = 60/10

》x = 6

• Breadth of rectangle = 2x = 2(6) = 12cm
• Length of rectangle = 3x = 3(6)= 18cm

Hence , Breadth of rectangle is 12cm

More Explanation :

• Perimeter of rectangle = 2(length + breadth)
• Area of rectangle = length × breadth
• Diagonal = √l² + b²

Answer 2

Given :-

• The perimeter of a square is double that of a reactangle
• Perimeter of square is 120
• Length and Breadth of a rectangle are in the ratio is 3 : 2

To find :-

• Find the Breadth of rectangle ?

★ $\large\underline{\frak{As~we~know~that,}}$

$\large\dag$ Formula Used :

• $\boxed{\bf{Perimeter~of~square~=~2~×~Perimeter~of~rectangle}}$

Solution :-

• Let the Length be 3x
• Let the Breadth be 2x

• The Perimeter of a square is double that of a reactangle

• Perimeter of square is 120

:$\implies$120 = 2 [2( l + b )]

$~~$:$\implies$120 = 2 [2( 3x + 2x )]

$~~~~~~$:$\implies$2( 3x + 2x ) = $\large{\sf{\frac{120}{2}}}$

$~~~~~~~~~~~$:$\implies$2( 3x + 2x ) = 60

$~~~~~~~~~~~~~~~~~$:$\implies$2( 5x ) = 60

$~~~~~~~~~~~~~~~~~~~~~$:$\implies$5x = $\large{\sf{\frac{60}{2}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$5x = ${\cancel{\dfrac{60}{2}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$5x = 30

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x = $\large{\sf{\frac{30}{5}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x = ${\cancel{\dfrac{30}{5}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\purple{\frak{x~=~6}}}}}$★

V E R I F I C A T I O N :

:$\implies$120 = 2 [2( 3x + 2x)]

$~~~~~$:$\implies$2( 3x + 2x ) = $\large{\sf{\frac{120}{2}}}$

$~~~~~~~~~~$:$\implies$2( 3x + 2x ) = ${\cancel{\dfrac{120}{2}}}$

$~~~~~~~~~~~~~~~$:$\implies$2( 3x + 2x ) = 60

$~~~~~~~~~~~~~~~~~~~~$:$\implies$2( 5x ) = 60

$~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$10x = 60

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x = $\large{\sf{\frac{60}{10}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x = ${\cancel{\dfrac{60}{10}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{x~=~6}}}}}$★

$\therefore$ Hence,

• Breadth of the reactangle is = $\large{\rm{2x}}$= $\large{\rm{2( 6 )}}$= $\large\underline{\rm{12~cm}}$
• Length of the rectangle is = $\large{\rm{3x}}$= $\large{\rm{3( 6 )}}$= $\large\underline{\rm{18~cm}}$

$\large\dag$ Hence Verified !!

• Breadth of the rectangle is = $\large\underline{\rm{12~cm}}$