Question

the length of a rectangle exceed it's breadth by 7 cm. if the length is decreased by 4 cm and breadth is increased by 3 cm the area of the new rectangle is same as the original rectangle. find length and breadth of original rectangle.​

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The length of a rectangle exceed it's breadth by 7 cm.

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

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

• The length and breadth of the original rectangle.

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

As we know that

The area of the rectangle is given by the formula:-

$\boxed{ \rm Area \: of \: rectangle = length \times breadth}$

According to the 1st condition:-

The length of a rectangle exceed it's breadth by 7 cm.

Let the breadth of the rectangle be x

The length of the rectangle = x + 7

The area of the rectangle

$\rm \implies length \times breadth$

$\rm \implies (x + 7)x$

$\rm \implies {x}^{2} + 7x$

Area of original rectangle = (x² + 7x)cm²

According to the 2nd condition:-

Length is decreased by 4cm

The length = x + 7 - 4 = x + 3

Breadth is increased by 3cm

The breadth = x + 3

The area of new rectangle

$\rm \implies length \times breadth$

$\rm \implies (x + 3)(x + 3)$

$\rm \implies {x}^{2} + 6x + 9$

The area of new rectangle = (x² + 6x + 9) cm²

Given

The area of new triangle = Area of original rectangle.

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

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

$\rm \implies - x = - 9$

$\rm \implies x = 9$

The breadth of rectangle = x = 9cm

The length of rectangle

= x + 7

= 9 + 7

= 16

$\underline{ \boxed{ \rm \pink{\therefore The \: length \: of \: rectangle=16cm}}}$

$\underline{ \boxed{ \rm \purple{\therefore The \: breadth \: of \: rectangle=9cm}}}$