Question

The difference b/w the lengh and the breadth of a rectangle is 8 cm and the perimeter is 64 cm. Find the length and breadth of the rectangle.​

Answer 1

• The length of the rectangle = 20 cm.
• The breadth of the rectangle = 12 cm.

Given :–

• The difference between the length and the breadth of the rectangle = 8 cm.

• The perimeter of the recatngle = 64 cm.

To Find :–

• The length and the breadth of the rectangle.

Solution :–

Let,

The length of the rectangle be x.

The breadth of the rectangle be y.

$\mapsto \sf x - y = 8 \: cm$ ––––(1)

Given that,

Perimeter of the rectangle = 64 cm

$\mapsto 2(length + breadth) = 64 cm$

$\mapsto 2(x + y) = 64 cm$

$\mapsto x + y \cancel\dfrac{64}{2} \: cm$

$\mapsto \sf x + y = 32 cm$ ––––(2)

Now, add both equation (1) and (2),

$\mapsto (x - y) + (x + y) = 8 \: cm+ 32 \: cm$

$\mapsto x - y + x + y = 40 \: cm$

$\mapsto x + x - y + y = 40 \: cm$

$\mapsto 2x = 40 \: cm$

$\mapsto x = \cancel \dfrac{40}{2} \: cm$

$\mapsto x = 20 \: cm$

Therefore, the length of the rectangle is 20 cm.

Now, substitute the value of x in equation (1),

$\mapsto x - y = 8 \: cm$

$\mapsto 20 \: cm - y = 8 \: cm$

$\mapsto 20\: cm -8 \: cm = y$

$\mapsto 12 \: cm = y$

$\mapsto y = 12 \: cm$

Therefore, the breadth of the rectangle is 12 cm.

Hence,

The length and the breadth of the rectangle is 20 cm and 12 cm.

Verification :–

Method 1 :

Perimeter of the recatangle = 64 cm.

I.e.,

2(length + breadth) = 64 cm

We have,

• Length = 20 cm.
• Breadth = 12 cm.

$\mapsto2(20 \: cm + 12 \: cm) = 64 \: cm$

$\mapsto2(32 \: cm) = 64 \: cm$

$\mapsto2 \times 32 \: cm = 64 \: cm$

$\mapsto64 \: cm = 64 \: cm$

Hence Verified !!

Method 2 :

Difference between the length and the breadth = 8 cm.

I.e.,

length – breadth = 8 cm.

We have,

• Length = 20 cm.
• Breadth = 12 cm.

$\mapsto20 \: cm - 12 \: cm = 8 \: cm$

$\mapsto8 \: cm = 8 \: cm$

Hence Verified !!

Answer 2

Hey buddy this is your answer
Actually place was not there ek might be clumsy but I’m giving u again that

Length =20cm
Breadth =12 cm


So this is the whole solution
Hope it is helpful
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