Question

The length of a rectangle is greater than the breadth by 3 cm if the lengthis increased by 9 cm. And breadth is reducedby 5 cm. The area remainsthe same find the dimensionsof the rectangle

Answer 1

AnswEr :

Let the length of Rectangle be x cm.

Breadth of Rectangle be (x - 3) cm.

If Length is increased by 9 cm and Breadth is reduced by 5 cm, then Area will be Same.

$\tt{New\: Dimensions} \begin{cases}\sf{Length=(x + 9)cm} \\ \sf{Breadth=(x - 3) - 5 } \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (x - 8) cm\end{cases}$

• According to the Question Now :

$\implies\tt{Area\:will \:be \: Same \:After \:Changing \: Dimensions}$

$\implies\tt{Area \: of \: Old \: Rectangle = Area \: of \: New \:Rectangle}$

$\implies\tt Length \times Breadth = New(Length \times Breadth)$

$\implies\tt x \times (x - 3) = (x +9 ) \times (x - 8)$

$\implies\tt {x}^{2} - 3x = x(x - 8) + 9(x - 8)$

$\implies\tt {x}^{2} - 3x = {x}^{2} - 8x + 9x - 72$

$\implies\tt \cancel{{x}^{2}} - 3x = \cancel{{x}^{2}} + x - 72$

$\implies\tt - 3x - x= - 72$

$\implies\tt - 4x= - 72$

$\implies\tt x = \cancel\dfrac{ - 72}{ - 4}$

$\implies \red{\boxed{\tt x =18}}$

$\rule{300}{1}$

$\underline{\star\:\text{Dimensions of the Rectangle are:}}$

$\leadsto \tt Length = x= \pink{18 cm}\\\leadsto\tt Breadth = (x-3) =(18 -3)= \pink{15cm}$

Answer 2

$\bf{\Huge{\underline{\boxed{\mathfrak{\green{ANSWER\::}}}}}}$

Given:

The length of a rectangle is greater than the breadth by 3cm, if the length is increased by 9cm & breadth is reduced by 5cm, the area remains same.

To find:

The dimensions of the rectangle.

$\bf{\Large{\underline{\rm{\red{Explanation\::}}}}}$

We know that area of rectangle= [length × breadth]  [sq.units]

• Let the length be R cm &

• Breadth be (R - 3)cm

A/q,

The length is increased by 9cm & breadth is reduced by 5cm;

• New length formed of rectangle= (R+9)cm
• New breadth formed of rectangle= (R-3-5)cm = (R-8)cm

The area remains the same;

⇒ Length × Breadth = New length × New breadth

⇒ R(R-3) = (R+9)(R-8)

⇒ R² - 3R = R² -8R + 9R - 72

⇒ $\cancel{R^{2}} -3R=\cancel{R^{2}} -8R+9R-72$

⇒ -3R = -8R + 9R -72

⇒ -3R = R - 72

⇒ -3R -R = -72

⇒ -4R = -72

⇒ R = $\cancel{\frac{-72}{-4} }$

⇒ R =18cm

Now,

• The dimensions of the rectangle:

Length of the rectangle,[R]= 18cm

Breadth of the rectangle,[R-3]= (18-3)cm= 15cm.