Question

the length of a rectangle exceeds its breadth of 7 cm. if the length agent 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 breadth of the original rectangle.

Answer 1

$\large{\bold{\underline{Solution :}}}$

Let the breadth be x

So, the length be (x + 7) cm

According to Question,

=> [(x + 7) - 4] × [x + 3] = x × (x + 7)

=> [x + 3] × [x + 3] = x² + 7x

=> x² + 3x + 3x + 9 = x ² + 7x

=> 6x - 7x = -9

=> - x = - 9

=> $\boxed{x = 9}$

$\bold{\underline{Note :}}$ x² = x² will be cut from both the sides

Length = (x + 7) cm
= (9 + 7) cm
= 16 cm

Hence, The length is 16 cm
& breadth is 9 cm

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$\boxed{Hope\:it\:helps!}$
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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 hops it helps you.