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 the new rectangle will be 70 sq. cm. more than that of the given rectangle. Find the dimensions of the rectangle.​

Answer 1

Answer:

breadth=15 length=18

Step-by-step explanation:

let the breadth be Xcm

so length= X+3= 18cm

adding 2cm to each

new breadth= X+2

new length= X+5

area of rectangle= L×B

as per condition

X(X+3) + 70= (X+2) (X+5)

solving the equation

we get

X= 15= breadth

X+3= length= 18

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: