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 a of the original triangle rectangle

Answer 1

Consider x= Breadth of the rectangle

Then x+7 = length of the rectangle

Given that" If the length is decreased by 4 cm and the breadth is increased by 3cm"

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

$(x+3)(x+3)=x^2+7x$

[tex] x^2+6x+9=x^2+7x [\tex]

Subtracting [tex] x^2 [\tex] on both sides,

[tex] 6x+9=7x [\tex]

Subtracting 6x on both sides,

[tex] 9=x [\tex] => Breadth of the rectangle=9 cm

Then the length of the rectangle [tex] = x+7=9+7=16 cm [\tex]

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.