Question

VERY URGENT - the length of a rectangle exceeds its breadth by 8 cm if length and breadth increase by 6 cm the area of the new rectangle will be 162 sq.cm more than the rectangle. Find the breadth of the given rectangle

Answer 1

Answer:

let the length be l and breadth be b

the new length be L and new breadth be B

A.T.Q

area = l.b

A = (8+b)b ....1

new area =L.B

162= (14+b)(b+6)

162 = 14b +84 +b^2 +6b

162= 20b + 84 + b^2

76 = 20b + b^2

b^2 + 20b -76 =0

after solving this eq u will get the breadth

Answer 2

Question:-

the length of a rectangle exceeds its breadth by 8 cm. if length and breadth increase by 6 cm the area of the new rectangle will be 162 sq.cm more than the given rectangle. Find the breadth of the given rectangle

Solution:-

Given:-

• The length of the rectangle exceeds it's breadth by 8 cm.

• If length and breadth is increased by

6 cm.

• Then area of new rectangle will be 162cm² 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 + 8 ........ ( 2 )

so, now....

for new rectangle

• breadth = B2 = x + 6 ........ (3)

• length = L2 = x + 8 + 6 ....... ( 4 )

we know, that area of new rectangle will be 162cm² more than given rectangle.

so now,

=> (Area of new rectangle)

- ( 162 cm² )

= (Area of oringinal rectangle)

=> (L2 × B2) - 162 = L1 × B1

=>( x + 8 + 6 ) ( x + 6 ) - 162

= ( x + 8 ) ( x )

=> ( x + 14) ( x + 6 ) - 162 = x² + 8x

=> x² + 6x + 14x + 84 - 162 = x² + 8x

=> x² + 20x -78 = x² + 8x

=> x² - x² + 20x - 8x - 78 = 0

=> 12x - 78 = 0

=> 12x = 78

=> x = 78/12

=> x = 6.5 cm

From ( 1 ),

• breadth = x = 6.5 cm.

From ( 2 ),

• length = x + 8

• length = 6.5 + 8

• length = 14.5cm.

Hence length and breadth of original rectangle is 6.5cm and 14.5cm respectively.

i hope it helps you.