Question

The length of a rectangle exceeds its breadth by 7. If the length is decreased by 4 cm and the breadth is increased by 3cm, 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 ​

Answer 1

Answer:

Step-by-step explanation:

$\underline{ \bf Given :-}$

The length of a rectangle exceeds its breadth by 7.

If the length is decreased by 4 cm and the breadth is increased by 3cm, the area of the new rectangle is the same as the area of the original rectangle.

$\underline{ \bf To \: Find \: :-}$

The length and the breadth of the original rectangle.

$\underline{ \bf Solution \: :-}$

Let the breadth of rectangle is x cm

And the length of rectangle is x + 7

And the Area be x(x + 7)

$\bf\underline{According \: to \: the \: Question :-}$

$\sf \implies(x+7-4)(x+3)=x(x+7)$

$\sf \implies(x+3)(x+3)=x^{2} +7x$

$\sf \implies(x+3)^2=x^{2} +7x$

$\sf \implies x^{2} +9+6x=x^{2} +7x$

$\sf \implies 6x+7x=-9$

$\sf \implies-x=-9$

$\bf \implies x=9$

$\bold{Length=x+7=9+7=16 \: cm}$

$\bold{Breadth=x=9 \: cm}$

Answer 2

Answer:

at first:

breadth =x

length=x+7

then,it is given that the length is decreased by 4cm and breadth is increased by 3cm.

Then, length=x+7-4

breadth=x+3

Again it is given that area of the new rectangle is same as the area of the original rectangle.

So, from this we get the equation that=

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

:- X²+ 7x =X² +7x-4x+3x+21-12

0= -x +9

-x=-9

x=9.

So, length and breadth of the original rectangle are=

length=x+7=16

breadth=x=9