Question

the perimeter of a rectangle is 40cm the length of the rectangle is less than double its breadth by 1cm find the length and breadth​

Answer 1

Answer:

Length of Rectangle = 13 cm

Breadth of Rectangle = 7 cm

Step-by-step explanation:

Given :

• Perimeter of rectangle = 40 cm

• Length of Rectangle is less than double its breadth by 1 cm ( 2x - 1 )

To find :

length and breadth of rectangle

• l = ?

• b = ?

Formulae Used :

Perimetre of Rectangle = 2 × ( l + b )

• l = length

• b = breadth

Solution :

let, breadth be x and length be 2x - 1

( substituting into formulae )

>>> 2 × ( l + b ) = 40 cm

>>> 2 × ( 2x - 1 + x ) = 40

>>> 4x - 2 + 2x = 40

>>> 6x - 2 = 40

>>> 6x = 40 + 2

>>> 6x = 42

>>> x = 42/6

>>> x = 7

So, Breadth ( x ) = 7 cm

Length = ( 2x - 1 )

= 2 × 7 -1

= 14 - 1 = 13 cm

Length = 13 cm

_____________________

Answer 2

Given:

• Perimeter of rectangle = 40 cm
• Length of rectangle is 1 cm less double of its breadth.

⠀⠀⠀⠀⠀⠀⠀

To find:

• Length and breadth of rectangle?

⠀⠀━━━━━━━━━━━━━━━━━━━━━

☯ Let breadth of Rectangle be x cm.

Therefore, Length of Rectangle is (2x - 1) cm.

⠀⠀⠀⠀⠀

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(1.8,-0.7)(0,4.2){2}{\sf\large (2x - 1) cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

⠀⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• Perimeter of rectangle = 40 cm

⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\purple{Perimeter_{\;(rectangle)} = 2(length + breadth)}}}}$

$:\implies\sf 2[(2x - 1) + x] = 40$

$:\implies\sf (2x - 1) + x = \cancel{ \dfrac{40}{2}}$

$:\implies\sf (2x - 1) + x = 20$

$:\implies\sf 3x - 1 = 20$

$:\implies\sf 3x = 20 + 1$

$:\implies\sf 3x = 21$

$:\implies\sf x = \cancel{ \dfrac{21}{3}}$

$:\implies{\underline{\boxed{\frak{\pink{x = 7}}}}}\;\bigstar$

Therefore,

⠀⠀⠀⠀⠀

• Breadth of Rectangle, x = 7 cm
• Length of Rectangle, (2x - 1) = 14 - 1 = 13 cm