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 new rectangle is the same as the area of the
original rectangle. Find the length and the breadth of the original rectangle.
please explain this
help me out of this please

Answer 1

Answer:

Let Breath=X cm

Then Length exceed 7 cm=(X+7)cm

Now Breath exceed by 3 =(X+3)cm

Now Length decrease by 4=(x+7-4)=(x+3)cm

Area = Length×breath

Question says both rectangle area is same

THEN a/q

x×(x+7)=(x+3)×(x+3)

x²+7x=x²+3x+3x+9

x²+7x-x²-3x-3x=9

7x-6x=9

x=9

So Breath is =9cm

Length=9+7=16cm

another rectangle Length =12cm

Breath=12cm

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

• breadth = 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.