Question

The length of a rectangle exceeds its breadth by 18 cm. If length and breadth are each increased by
6 cm. then area of the new rectangle will be 336 cm square more than that of the given rectangle. Find the
length and breadth of the given rectangle.​

Answer 1

Let the Breath be x

Then,length=x+18

Increased length = x+18+6

= x+24

Increased Breath= x+6

Area of the given rect.= x*x+18

= x^2+18

Area of the increased rectangle=

(x+24)*(x+6)

=x^2 + 30x + 144

Now,Difference=336(given)

Therefore,(x^2+30x+144)-(x^2+18)=336

30x + 126 = 336

30x = 336 - 126

30x = 210

× = 210/30

= 7 cm.

Breadth of the given rectangle = x = 7 cm.

Length of the given rectangle. = (×+18)

= (7+18)

= 25cm. ANS.

Answer 2

Question:-

The length of a rectangle exceeds its breadth by 18 cm. If length and breadth are each increased by

6 cm. then area of the new rectangle will be 336 cm square more than that of the given rectangle. Find the

length and breadth of the given rectangle.

Solution:-

given:-

• The length of the rectangle exceeds it's breadth by 18 cm.

• If length and breadth is increased by 6 cm.

• Then area of new rectangle will be 336cm² more than given rectangle.

Find:-

• The length and breadth of the original rectangle = ?

Formula:-

=> Area of rectangle

= length(L) × breadth(B)

Now, by given,

let, x be the breadth of rectangle so,

for original rectangle.

• breadth = B1 = x ........ ( 1 )

• length = L1 = x + 18 ........ ( 2 )

so, now....

for new rectangle

• breadth = B2 = x + 6 ........ (3)

• length = L2 = x + 18 + 6 ....... ( 4 )

we know, that area of new rectangle will be 336cm² more than given rectangle.

so now,

=> (Area of new rectangle) - ( 336 cm² )

= (Area of oringinal rectangle)

=> (L2 × B2)+ 336 = L1 × B1

=>( x + 18 + 6 ) ( x + 6 ) - 336 = ( x + 18) ( x )

=> ( x + 24) ( x + 6 ) - 336 = x² + 18x

=> x² + 24x + 6x + 144 - 336 = x² + 18x

=> x² + 30x + 292 = x² + 18x

=> x² - x² + 30x - 18x - 292 = 0

=> 12x - 292 = 0

=> 12x = 292

=> x = 292/12

=> x = 24.33cm

From ( 1 ),

• breadth = x = 24.33cm

From ( 2 ),

• length = x + 18

• length = 24.33 + 18

• length = 42.33cm

From ( 3 )

• breadth = x + 6

• breadth = 24.33 + 6

• breadth = 30.33cm

From ( 4 )

• length = x + 18 + 6

• length = 24.33 + 22

• length = 46.33cm

Hence length and breadth of original rectangle are 42.33 cm

and 24.33 cm respectively.

and length and breadth of new rectangle are 46.33 cm and

30.33 cm respectively.

i hope it helps you.