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?

Answer 1

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.

Answer 2

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 : -

`\pink{\boxed{Perimeter \: of \: rectangle = 2(l + b)}}`

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

`\purple{ \boxed{Therefore, \: breadth \: is \: of \: 9 \: cm }}`

Now , Length of rectangular sheet is equal to ,

• x + 3

• 9 + 3

• 12

`\red{ \boxed{Therefore, \: length \: is \: of \: 12 \: cm }}`

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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