Question

18. The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each increase
by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. Find the
length and breadth of the given rectangle.​

Answer 1

Given, L=B+3,

as per the 2nd condition

Area=(L+2)(B+2)=70

here L=B+3

so above equation becomes

(B+5)B+2)=70

B²+7B+10=70

B²+7B-60=0

solving this quadratic equation, we get

B²+12B-5B-60=0

B=-12 which is not possible

or B=5cm which is true

so L=8cm.

Answer 2

Answer:

Let be the breadth x

length =x+3

according to the question if we compare the rectangle's area to the new rectangle's area the difference will be 70sq cm

area of the first rectangle =

x ( x + 3 )

= $x^{2}$ + 3x

after adding 2cm to length and breadth will x + 3 + 2 and x + 2

area of the new rectangle =

( x + 3 + 2 ) ( x + 2 )

( x + 5) ( x + 2 )

x ( x + 2 ) + 5 ( x + 2 )

$x^{2}$ + 2x + 5x + 10

= $x^{2}$ + 7x + 10

according to the question

( $x^{2}$ + 7x + 10 ) - ( $x^{2}$ + 3x ) = 70

$x^{2}$ + 7x + 10 - $x^{2}$ - 3x = 70

$x^{2}$ - $x^{2}$  + 7x - 3x + 10 = 70

4x + 10 = 70

4x = 70 - 10

4x = 60

x = 15

length of rectangle = 18 cm

breadth of rectangle = 15 cm

Step-by-step explanation: