Question

if the length of a rectangle is increased by 10 cm and breadth decreased by 5 cm, the area remain unchanged. if the length is decreased by 5 cm and the breadth is increased by 4 cm, even the area remain unchanged.find the dimension of the rectangle.

Answer 1

$\textbf{Answer}$

Suppose the length of a rectangle = x cm

Suppose the breadth of a rectangle = y cm

We know that,
$\textbf{Area of rectangle = length * breadth}$

=> Area of a rectangle = xy cm^

$\textbf{According to the question,}$
If length is increased by 10 and breadth is decreased by 5,
Area = (x+10) × (y-5)
=> xy = xy - 5x + 10y - 50
=> $\textbf{5x - 10y = -50 -----(1)}$

$\textbf{According to the question,}$
If length is decreased by 5 and breadth is increased by t,
Area = (x-5) × (y+4)
=> xy = xy + 4x - 5y - 20
=> $\textbf{4x - 5y = 20 ------(2)}$

Lets solve equations (1) and (2) now.

Lets multiply equation (2) with 2
&
Then subtract equation (2) by equation (1),

=> (5x - 10y) - 2(4x - 5y) = -50 - 2(20)

=> 5x - 8x - 10y + 10y = - 90

=> -3x = -90

=> x = 30

Lets put the value of x in equation (1),
=> 5x - 10y = - 50
=> 5(30) - 10y = - 50
=> 150 - 10y = - 50
=> - 10y = - 50 - 150
=> - 10y = - 200
=> y = 200/10
=> y = 20

So the area is,
=> xy = 30 × 20
=> xy = 600 cm^2

$\textbf{Length of a rectangle is 30 cm}$
$\textbf{Breadth of a rectangle is 20 cm}$
$\textbf{Area of a rectangle is 600 cm2}$

$\textbf{Hope My Answer Helped}$

$\textbf{Thanks}$

Answer 2

Suppose the length of a rectangle = x cm

Suppose the breadth of a rectangle = y cm

We know that,
\textbf{Area of rectangle = length * breadth}Area of rectangle = length * breadth

=> Area of a rectangle = xy cm^

\textbf{According to the question,}According to the question, 
If length is increased by 10 and breadth is decreased by 5,
Area = (x+10) × (y-5)
=> xy = xy - 5x + 10y - 50
=> \textbf{5x - 10y = -50 -----(1)}5x - 10y = -50 —–(1) 

\textbf{According to the question,}According to the question, 
If length is decreased by 5 and breadth is increased by t,
Area = (x-5) × (y+4)
=> xy = xy + 4x - 5y - 20
=> \textbf{4x - 5y = 20 ------(2)}4x - 5y = 20 ——(2) 

Lets solve equations (1) and (2) now.

Lets multiply equation (2) with 2
&
Then subtract equation (2) by equation (1),

=> (5x - 10y) - 2(4x - 5y) = -50 - 2(20)

=> 5x - 8x - 10y + 10y = - 90

=> -3x = -90

=> x = 30

Lets put the value of x in equation (1),
=> 5x - 10y = - 50
=> 5(30) - 10y = - 50
=> 150 - 10y = - 50
=> - 10y = - 50 - 150
=> - 10y = - 200
=> y = 200/10
=> y = 20

So the area is,
=> xy = 30 × 20
=> xy = 600 cm^2

\textbf{Length of a rectangle is 30 cm}Length of a rectangle is 30 cm 
\textbf{Breadth of a rectangle is 20 cm}Breadth of a rectangle is 20 cm 
\textbf{Area of a rectangle is 600 cm2}Area of a rectangle is 600 cm2