Question

The length of a rectangle is greater than the breadth by 3cm .If the length is increased by 9cm and the breadth is reduced by 5cm,the area remains the same. Find the dimensions of the rectangle ​

Answer 1

Answer:

Let the breadth of rectangle be x cm.

Then the length of rectangle will be

(x + 3) cm.

We know that , area of rectangle is given by;

Area = length•breadth

Thus,

Initial area = x(x+3) cm^2

Now;

New length after increasing it by 9 cm

= (x+3+9) cm

= (x + 12) cm

Also;

New breadth after reduced it by 5cm

= (x-5) cm

Thus,

Final area = (x-5)(x+12) cm^2

According to the question;

=> Initial area = Final area

=> x(x+3) = (x-5)(x+12)

=> x^2 + 3x = x^2 + 12x - 5x - 60

=> 12x - 5x - 3x = 60

=> 4x = 60

=> x = 60/4

=> x = 15

Thus,

Breadth of the rectangle = x cm

= 15 cm

Length of the rectangle = (x+3) cm

= (15+3) cm

= 18 cm

Hence, the length and the breadth of the rectangle are 18 cm and 15 cm respectively.

Answer 2

Answer :-

Dimensions of the rectangle are 18 cm and 15 cm.

Explanation :-

Let the breadth of the rectangle be x cm

Length of the rectangle = 3 cm more than the breadth = (x + 3) cm

Area of the reactangle = Length * Breadth = x(x + 3) = x² + 3x

Given

If Length is increased.by 9 cm and breadth is reduced by by 5 cm the area remains the same

⇒ {(x + 3) + 9}(x - 5) = x² + 3x

⇒ (x + 3 + 9)(x - 5) = x² + 3x

⇒ (x + 12)(x - 5) = x² + 3x

⇒ x(x - 5) + 12(x - 5) = x² + 3x

⇒ x² - 5x + 12x - 60 = x² + 3x

⇒ x² + 7x - 60 = x² + 3x

⇒ x² + 7x - x² - 3x = 60

⇒ 4x = 60

⇒ x = 60/4

⇒ x = 15

Breadth of the rectangle = x = 15 cm

Length of the rectangle = (x + 3) = (15 + 3) = 18 cm

∴ the dimensions of the rectangle are 18 cm and 15 cm.