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 81cm² more than that of the given
rectangle. Find the length and breadth of the given rectangle.​

Answer 1

Step-by-step explanation:

let breadth be x and the length be 4+x

Area = l×b = (4+x) × x

= 4x + x^2

if the lenght and breadth increase by 3 then

length=4+x+3

breadth=x+3

Then it's area= (4+x+3) × (x+3)

= (7+x) × (x+3)

= x(7+x) + 3( 7+x)

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

= 10x +x^2 + 21

10x + x^2+21 = 4x + x^2 + 81 (cancel x^2)

10x - 4x = 81

6x = 81

x = 81÷6= 13.5cm

hence, breadth =13.5cm and length= 4+13.5

=17.5cm

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