Question

the length of a rectangle exceeds its breadth by 4 cm. if the length and breadth are increased by 3 cm each, the area of new rectangle will be 81 sq cm more than that of the given rectangle.find the length and breadth of the given rectangle.

Answer 1

so breadth = 10
length = b+4=14

Answer 2

$\bold{\underline{\underline{Solution}}}$

Let we consider the length of rectangle be x

$\bold{\underline{Case \: 1}}$

Length of rectangle be x

Length of rectangle $\bold{exceed}$its breadth by 4 cm

So , Breadth of rectangle be (x - 4)

Area of reactangle = $\bold{A_1}$

length × breadth = $\bold{A_1}$

x ( x - 4 ) = $\bold{A_1}$

$\bold{A_1}$ = x² - 4x ........(equation 1)

$\bold{\underline{Case\: 2}}$

Now the length and breadth of new rectangle

In a case it's given that both are $\bold{increased}$ by $\bold{3\: cm}$

Length of new rectangle = (x + 3)

Breadth of new rectangle = (x - 4 + 3) = (x - 1)

Area of new rectangle = ($\bold{A_1}$ + 81)

length × breadth = ($\bold{A_1}$ + 81)

( x + 3 )( x - 1 ) = ($\bold{A_1}$ + 81)

x² - x + 3x - 3 = ($\bold{A_1}$ + 81)

x² + 2x - 3 = ($\bold{A_1}$ + 81)

$\bold{A_1}$ = x² + 2x - 3 -81

$\bold{A_1}$ = x² + 2x - 84 ......(equation 2)

Equate the equation (1) & (2)

x² - 4x = x² + 2x -84

-(4x + 2x) = -84

-6x = -84

x = $\bold{\dfrac{84}{6}}$

x = $\bold{14 \: cm}$

So the length of original and first rectangle is

Length of rectangle = x = 14 cm

Breadth of rectangle = ( x - 4 ) = ( 14 - 4 ) = 10 cm

$\bold{\underline{Answer}}$

$\bold{ length \: of \: rectangle \: = \: 14 \: cm}$

$\bold{ breadth \: of \: rectangle \: = \: 10 \: cm}$


$\bold{Thanks}$