Question

the length of a rectangle exceeds its breath by 4 cm if length and breadth are increased by 7 cm and 3 cm respectively ,then the area of the new rectangle will be 81 cm square more than that of the given rectangle find the length and breath of the given rectangle​

Answer 1

Answer:

length = 8.8 cm breadth = 4.8 cm

Step-by-step explanation:

case 1

l = b + 4 cm

b= b cm

A1= ( b+4) b

= b^2 + 4b

case 2

l = b + 4 + 7 cm

b= b + 3 cm

A2= ( b + 11 ) (b + 3)

= b^2 + 11b + 3b + 33

=b^2 + 14b + 33

but given

A2= A1 + 81 cm

b^2 + 14b + 33 = b^2 + 4b + 81

b^2 - b^2 + 14b - 4b = 81 - 33

10b = 48

b = 4.8 cm

and l = 4.8 + 4 = 8.8. cm

Answer 2

Given data :-

• The length of a rectangle exceeds its breadth by 4 cm.

• Length and breadth are increased by 7 cm and 3 cm respectively.

• The area of the new rectangle will be 81 cm² more than that of the given rectangle.

Solution :-

{For given rectangle}

Let, breadth of given rectangle be x cm

→ Breadth, B = x cm ....( 1 )

Hence, according to given

→ Length, L = ( x + 4 ) cm ....( 2 )

Now, {For new rectangle}

→ Length, L' = ( x + 4 + 7 ) cm

→ Breadth, B' = ( x + 3 ) cm

Now, according to given

→ Area of new rectangle = Area of given rectangle + 81 cm²

{we use formula of area of rectangle}

→ L' * B' = [ L * B ] + 81

→(x + 4 + 7) * (x + 3) = [x * (x + 4)] + 81

→ [ ( x + 11 ) * ( x + 3 ) ] = [x² + 4x] + 81

→ [ x² + 3x + 11x + 33 ] = x² + 4x + 81

→ x² + 14x + 33 = x² + 4x + 81

→ x² - x² + 14x - 4x = 81 - 33

→ 10x = 48

→ x = 48/10

→ x = 4.8 cm

{ from eq. ( 1 ) }

Breadth of given rectangle is 4.8cm.

{ from eq. ( 2 ) }

→ Length = ( x + 4 ) cm

→ Length = ( 4.8 + 4 ) cm

→ Length = 8.8 cm

Length of given rectangle is 8.8cm.

Answer : Hence, Length of given rectangle is 8.8 cm and Breadth of given rectangle is 4.8 cm.

{Note: ( * ) sign used for multipliclation }