Question

The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each increased 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 that
length of the rectangle = breadth + 3

let breadth of the rectangle be x cm.
so, the length of the rectangle will be (x+ 3)cm
case 1st..

area of the rectangle= x(x+3)
A1 = (x^2 + 3x) sq. cm

case 2nd..

according to ques.

new length = 3+x+2
= (5+x)cm
and new breadth= (x+2)cm
so,
new area = (x+2)(5+x)
A2 = x^2 + 7x + 10 sq. cm

according to question

A1 + 70 = A2
x^2+3x + 70 = x^2 +7x+ 10
3x +70 = 7x +10
60=4x
x= 60/4
x= 15cm

hence ,
breadth= x = 15 cm
length= x+3= 15+3 = 18 cm

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: