Question

2. A rectangle has a perimeter measuring 64 cm. The length is 4 cm
more than 3 times the breadth. Find the dimensions of the
rectangle.​

Answer 1

ANSWER :

Dimensions are 25 cm and 7 cm.

EXPLANATION :

GIVEN :-

• Perimeter of rectangle is 64 cm.
• The length is 4cm more than 3 times the breadth.

TO FIND :

• Dimensions of the rectangle.

SOLUTION :

Let the breadth of the rectangle be x cm.

Length is 4 cm more than 3 times the breadth.

Length = (3x + 4) cm

We know,

${\boxed{\sf{Perimeter\:of\: rectangle=2(Length+Breadth)}}}$

Perimeter = 2(3x+4+x) cm

→ Perimeter = 2(4x+4) cm

→ Perimeter = 8(x+1) cm

★ According to the question,

$\sf{\:\:\:\:\:8(x+1)=64}$

$\implies\sf{x+1=\frac{64}{8}}$

$\implies\sf{x+1=8}$

$\implies\sf{x=8-1}$

$\implies\sf{x=7}$

Breadth = 7 cm.

Length = (3 × 7 + 4 ) cm

→ Length = 25 cm

Therefore ,dimensions are 25 cm and 7 cm.

_____________________

★VERIFICATION :

Length of rectangle = 25 cm.

Breadth of rectangle = 7 cm.

Perimeter of rectangle=2(25+7) cm

→ Perimeter of rectangle= 64 cm.

Hence verified___!!

______________________

Answer 2

Given :

• Perimeter of the rectangle = 64 cm.

• The length is 4 cm more than 3 times the breadth.

To find :

• The dimensions of the rectangle =?

Step-by-step explanation:

Perimeter of the rectangle = 64 cm [Given]

Let, The Breadth of the rectangle be x.

Then, The length is 4 cm more than 3 times the breadth be 3x + 4.

We know that,

Perimeter of the rectangle = 2 ( Length + Breadth)

Substituting the values in the above formula, we get,

➮ 64 = 2 ( 3x + 4 + x)

➮ 64 = 2 ( 4x + 4 )

➮ 64 = 8x + 8

Or, 8x + 8 = 64

➮ 8x = 64 - 8

➮ 8x = 56

➮ x = 56/8

➮ x = 7.

Thus, The Breadth of the rectangle x = 7 cm.

Now,

The length of the rectangle, 3x + 4

So, 3x + 4

= 3 × 7 + 4 [x = 7]

= 21 + 4

= 25

Now clearly,

Lenght of the rectangle = 25 cm

Breadth of the rectangle = 7 cm.

Verification :

We know that,

The sum of length, breadth and twice of the length, breadth = Perimeter of the rectangle

So,

2(Lenght + Breadth) = 64

Now, After Substituting the values, we get,

➮ 2 ( 25 + 7) = 64

➮ 2 × 32 = 64

➮ 64 = 64

L. H. S = R. H. S

Hence, it is verified.