Question

The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.
pls tell tomorrow is my exam​

Answer 1

Perimeter = 240 cm

Let x be the length & y be the breadth

ATQ

2( x + y ) = 240

⇒ x + y = 120 ________ ( 1 )

Length increased by 10%

New length :-

$\sf{\footnotesize={x+{\dfrac{10}{100}}x}}$

$\sf{\footnotesize={\dfrac{100x+10x}{100}}}$

$\sf{\footnotesize={\dfrac{11x}{10}}}$

Breadth decreased by 20%

New breadth :-

$\sf{\footnotesize={y-{\dfrac{20}{100}}y}}$

$\sf{\footnotesize={\dfrac{100y-20y}{100}}}$

$\sf{\footnotesize={\dfrac{80y}{100}}}$

$\sf{\footnotesize={\dfrac{8y}{10}}}$

With new length & breadth , we get same perimeter .

So ,

$\sf{\footnotesize⇒{2\left({\dfrac{11}{10}}x+ {\dfrac{8}{10}}y\right)}=240}$

$\sf{\footnotesize⇒{\dfrac{11}{10}}x+{\dfrac{8}{10}}y = 120}$

$\sf{\footnotesize⇒{11x+8y=1200}}$ _______ (2)

Now , (second eqn.) - 8 × (first eqn.) , we get

3x = 240

⇒x = 80

putting the value of x in first equation ,

y = 120 - 80

⇒y = 40

So , length = x = 80 cm

and breadth = y = 40 cm