Question

the length of the rectangle exceeds it's breadth by 3 cm. if the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70sq.cm more than of the given rectangle. find the length and breadth of the given rectangle​

Answer 1

Step-by-step explanation:

Let the length and breadth of the rectangle be 'l' and 'b' respectively.

l=b+3

A=lb=(b+3)(b)=b²+3b

if the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70sq.cm more than of the given rectangle:

(b+3+2)(b+2)=b²+3b+70

b(b+5) +2(b+5) = b²+3b+70

b²+5b+2b+10=b²+3b+70

7b+10=3b+70

7b-3b=70-10

4b=60

b=60/4 =15cm

l=b+3 =15+3 = 18cm

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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: