Respuesta :

Answer:

Let the breadth be x cm

Length be (x+3) cm

Perimeter of Rectangular Sheet of Paper is 42 cm

Perimeter of Sheet = 2 (Length+ breadth)

42 = 2 ( x + x + 3)

42 = 2(2x+3)

42 = 4x + 6

42 -6 = 4x

36 = 4x

36/4 = x

9 = x

Length = 9+3 = 12 cm

So, the length of Rectangular Sheet of paper is 12 cm.

TheAmethyst

Question : -

The length of rectangular sheet of paper is 3cm more than its breadth.The sheet of paper has a perimeter of 42cm. what is its length ?

Given : -

  • Length = 3 cm more than its breadth

  • Perimeter of sheet = 42 cm

To Find : -

We have to find the length of rectangular sheet .

Formula Used : -

[tex] \pink{\boxed{Perimeter \: of \: rectangle = 2(l + b)}}[/tex]

Where ,

  • l = length of rectangular sheet.

  • b = breadth of rectangle sheet.

Concept : -

The concept of this question goes with perimeter of rectangle by making suitable equation with the help of given length and breadth .

To Assume : -

We are assuming breadth of as x cm and,

Length of given rectangular sheet is 3 cm more than its breadth . So length is x + 3 cm .

Let's Start Solving : -

As given perimeter of rectangular sheet is 42 cm and perimeter formula for rectangle is 2 ( l + b ) . So equating the given perimeter with perimeter formula :

  • 2 ( l + b ) = 42

Now ,substituting value of length and breadth in it :

  • 2 [ ( x + 3 ) + x ] = 42

Now , transposing 2 to right hand side :

  • x + 3 + x = 42/2

By dividing 42 by 2 we get :

  • x + 3 + x = 21

Now, adding x with x :

  • 2x + 3 = 21

Now , transposing 3 to right hand side :

  • 2x = 21 - 3

Now , subtracting 3 from 21 :

  • 2x = 18

Now , transposing 2 to right hand side :

  • x = 18/2

Now , dividing 18 by 2

  • x = 9

[tex] \purple{ \boxed{Therefore, \: breadth \: is \: of \: 9 \: cm }}[/tex]

Now , Length of rectangular sheet is equal to ,

  • x + 3

  • 9 + 3

  • 12

[tex]\red{ \boxed{Therefore, \: length \: is \: of \: 12 \: cm }}[/tex]

Verification :

Verifying our answer by putting values of length and breadth in perimeter and formula and it must be equal to 42 cm as it is given in the question :

  • 2 ( l + b ) = 42

  • 2 ( 12 + 9 ) = 42

  • 2 ( 21 ) = 42

  • 42 = 42

  • L.H.S = R.H.S

  • Hence, Verified .

Therefore, our values for length and breadth are correct .

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