Question

The length of a rectangle is greater than 4 times its breadth by 5cm. If its length is reduced by 2cm and breadth is increased by 2cm, then the area of the rectangle increases by 36cm². Find the length and breadth of the original rectangle.

Answer 1

Here, let the breadth be x cm,

Then the length is 4x + 5cm (since it’s 5cm more than 4 times its breadth)

Given conditions:

If the length is reduced by 2cm and the breadth is increased by 2cm, the area increases by 36cm².

So we write it in the form of an equation:

(4x + 5 − 2)(x + 2) = (4x + 5)x + 36

(4x + 3)(x + 2) = 4x² + 5x + 36

4x(x + 2) + 3(x + 2) = 4x² + 5x + 36

4x² + 8x + 3x +6 = 4x² + 5x + 36

4x² + 11x + 6 = 4x² + 5x + 36

4x² − 4x² + 11x − 5x = 36 − 6

6x = 30

x = `30/6`

∴ x = 5

Now, finding the dimensions:

Breadth = x = 5cm

Length = 4x + 5 

= 4(5) + 5

= 25cm

Hence, the length and breadth of the original rectangle are 25cm and 5cm.