Question

The length of a rectangle exceeds its breadth by 4 cm. If length and breadth are increased by 3 cm each the area of the new rectangle will be 81 square.cm more than of the given rectangle. find the length and breadth of the given rectangle. ​

Answer 1

Step-by-step explanation:

Given that the length of a rectangle exceeds its breadth by 4 cm . if length and breadth are each is increased by 3 cm , the area of the new rectangle is 81 square cm more than the given rectangle

Answer 2

Given data:-

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

• The length and breadth are increased by 3 cm.

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

Solution:-

Here, { Length = L & Breadth = B & Area = A}

• Let, A be the area of given rectangle &

A° be the area of new rectangle.

• Let, L & B the length & breadth of given rectangle & L° & B° the length & breadth of new rectangle.

Now, for given rectangle

Let, x be the breadth of rectangle.

—› B = ' x ' .....( 1 )

Hence, according to given,

—› L = ( x + 4 ) .......( 2 )

Now, for new rectangle, {from given}

—› L° = ( x + 4 + 3 ) = (x + 7) .......( 3 )

—› B° = ( x + 3 ) ......( 4 )

Now, { from given }

—› A° = A + 81 cm²

{ We know, formula area of rectangle

—› Area of rectangle = L × B }

—› A° = [ L × B ] + 81 cm²

—› L° × B° = [ L × B ] + 81 cm²

{ from ( 1 ), ( 2 ), ( 3 ) & ( 4 )}

—› ( x + 7 ) × ( x + 3 )= [x ( x + 4 )] + 81

—› x² + 3x + 7x + 21 = [x² + 4x] + 81

—› x² + 10x + 21 = x² + 4x + 81

—› x² - x² + 10x - 4x = 81 - 21

—› 6x = 60

—› x = 60/6

—› x = 10 ...... ( 5 )

Hence, from eq. ( 1 ) Breadth of given rectangle is 10 cm.

Now, from eq. ( 2 ) & ( 5 )

—› L = x + 4

—› L = 10 + 4

—› L = 14

Hence, from length of given rectangle is 14 cm.

The length and breadth of given rectangle are 14 cm & 10 cm respectively.