Question

the length of a rectangle exceeds its breadth by 7 cm if the length is decreased by 4 cm and the breadth is increased by 3 cm the area of the rectangle is the same as the area of the original rectangle. find the length and the breadth of the original rectangle.

Answer 1

let length be x and breadth be y

the length of a rectangle exceeds its breadth by 7 cm
so, x = y + 7............(1)

area of rectangle = y(y + 7) = y² + 7y.......(2)

the length is decreased by 4 cm and the breadth is increased by 3 cm
so, length = x - 4 = y + 7 - 4 = y + 3
breadth = y + 3

area of rectangle = (y + 3)(y + 3) = y² + 3y + 3y + 9 = y² + 6y +9......(3)

the area of the rectangle is the same as the area of the original rectangle
so, equate (3) and (2)
y² + 7y = y² + 6y + 9
y = 9

substitute y in (1)
x = 9 + 7 = 16

so, length is x = 16 and breadth is 9 of original rectangle

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Answer 2

Solution:-

given:-

• The length of the rectangle exceeds it's breadth by 7cm.

• If the length is decreased by 4cm and the breadth is increased by 3cm.

• The area of new rectangle is the same as the area of original 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 + 7 ........ ( 2 )

so, now....

for new rectangle

• breadth = B2 = x + 3 ........ (3)

• length = L2 = x + 7 - 4 ....... ( 4 )

we know,

=> (Area of new rectangle) = (Area of oringinal rectangle)

=> L2 × B2 = L1 × B1

=>( x + 7 - 4 ) ( x + 3 ) = ( x + 7) ( x )

=> ( x + 3 ) ( x + 3 ) = x² + 7x

=> ( x + 3 )² = x² + 7x

=> x² + 6x + 9 = x² + 7x

=> x² - x² + 6x - 7x + 9 = 0

=> - x + 9 = 0

=> - x = - 9

=> x = 9

From ( 1 ),

• breadth = x = 9 cm.

From ( 2 ),

• length = x + 7

• length = 9 + 7

• length = 16 cm.

Hence length and breadth of

original rectangle is 16cm and

9cm respectively.

i hope it helps you.