Question

. A 164 cm long rod is to be bend to make a rectangle . Its length should be 2 cm more than three times its breadth . a) What should be the perimeter of the rectangle ? b) What should be the length and the breadth ?

Answer 1

Answer:

Length => 62

Breath => 20

Perimeter => 164

Explanation:

Given :

• A 164cm long rod is to be bend to make a rectangle and length is 2cm more than three times it’s breadth.

To Find :

• Perimeter of the rectangle

• Length and the breadth of the rectangle.

Solution :

Let the breadth be “x”

Length of the rectangle => 2 + 3(x)

Perimeter of the rectangle :-

$\rightarrow \sf{}2(length+breath)=164$

$\rightarrow \sf{}2(2+3x+x)=164$

$\rightarrow \sf{}2(2+4x)=164$

$\rightarrow \sf{}4+8x=164$

$\rightarrow \sf{}8x=164-4$

$\rightarrow \sf{}8x=160$

$\rightarrow \sf{}x=\dfrac{160}8}$

$\rightarrow \sf{}x=20$

Here,x = 20 = breath.

Therefore,length = 2 + 3(x)

=> 2 + 3(20)

=> 2 + 60

=> 62

Hence,

Length => 62

Breath => 20

Perimeter => 164  

Answer 2

Given :-

• The length of rod = 164 cm

To FinD :-

• The perimeter of the rectangle

• The length and breadth of rectangle.

Solution :-

(a) The perimeter of the rectangle will be the length of the rod.

So the perimeter of the rectangle = 164 cm.

___________________________________

(b) Let the breadth of the rectangle is 'x'

So, according to the question →

Length of the rectangle = 2 + 3x

We know that →

• Perimeter of rectangle = 2( Length + breadth)

$\rightarrow{2( 2 + 3x + x ) = 164 }$

$\rightarrow{2( 2 + 4x ) = 164}$

$\rightarrow{2+4x=\frac{164}{2}}$

$\rightarrow{2+4x=82}$

$\rightarrow{4x=82-2}$

$\rightarrow{4x=80}$

$\rightarrow{x=\frac{80}{4}}$

$\rightarrow{x=20}$

So, the breadth of the rectangle = 20

The length of the rectangle = 2 + 3x

$\rightarrow{ 2 + 3 × 20 }$

$\rightarrow{ 2 + 60 }$

$\rightarrow{62}$