Question

The Length of a rectangle exceeds its breadth by 4 cm. If Length and Breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle. Find the length and breadth of the given rectangle.​

Answer 1

Answer :-

The length of Rectangle = 14cm.

Breadth of Rectangle = 10cm.

Step-by-step explanation:

To Find :-

• The length and breadth of rectangle.

★ Solution

Given the,

The length of Rectangle exceeds it's breadth by 4m.

Assumption

Let us assume the breadth of rectangle as (x) cm and the length of rectangle as (x + 4)cm .

Also given,

Length and breadth are increased by 3cm .

∴ Length = (x + 4) + 3 = (x + 7)m ; Breadth = (x + 3)m .

We know,

Area of rectangle = lb sq. units,

Where,

• l = Length
• b = Breadth

According the question,

⇒ (x + 7) (x + 3) = 81 + (x) (x + 4)

⇒ x² + 7x + 3x + 21 = 81 + x² + 4x

⇒ x² + 10x + 21 = 81 + x² + 4x

⇒ 10x + 21 = 81 + 4x

⇒ 10x - 4x = 81 - 21

⇒ 6x = 60

⇒ x = 60/6

⇒ x = 60

We got, The value of x is 60.

Now, The length and breadth of rectangle :-

⇒ Length = (x + 4) = (10 + 4) = 14m

⇒ Breadth = (x) = 10m

∴ The length and breadth of rectangle is 14m and 10m.