Question

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

Answer 1

Solution :-

Let the breadth be x ;

Length = x + 4.

Area of Rectangle = L × b

-> x (x + 4)

-> x² + 4x

If length & breadth are increased by 3, then :-

Length = x + 4 + 3

Breadth = x + 3

According To The Question :-

Area of rectangle = x² + 4x + 81

-> (x + 3) × (x + 4 + 3) = x² + 4x + 81

-> (x + 3) × (x + 7) = x² + 4x + 81

-> x² + 10x + 21 = x² + 4x + 81

-> x² - x² + 10x - 4x = 81 - 21

-> 6x = 60

-> x = 10

Breadth = 10 cm ;

Length = 10 + 4 = 14 cm.

So, the length of rectangle is 14 cm ;

The breadth of rectangle is 10 cm.

Answer 2

Let the breath of the rectangle be x

Then, length = x+4

Area of the rectangle = length × breadth

= (x+4)x

= x^2 + 4x

If the length and the breadth are increased by 3 cm each then,

New Length = x+4+3 = x+7

New Breadth = x+3

New rectangle's area = length × breadth

= (x+7)(x+3)

= x^2 + 3x + 7x + 21

= x^2 + 10x + 21

As given, that the new area is 81 sq. cm more than the original rectangle's area.

Therefore,

=> x^2 + 10x + 21 = x^2 + 4x + 81

=> 10x + 21 = 4x + 81 [as x^2 of both sides are cancelled]

=> 10x - 4x = 81 - 21

=> 6x = 60

=> x = 60/6

=> x = 10

Therefore,

Length = x + 4

= (10 + 4) cm

= 14 cm

Breadth = x

= 10 cm

HOPE THIS HELPS...