Question

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

Answer 1

Answer:

prefer to it child!!!

Step-by-step explanation:

therefore,. l=80

Answer 2

Solution :

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

The perimeter of a rectangle is 240 cm. If it's length is decreased by 10% & it's breadth is increased by 20% we get the same perimeter .

$\underline{\bf{Explanation\::}}$

Let the length of a rectangle be r cm & the breadth of a rectangle be m cm respectively;

As we know that formula of the perimeter of rectangle;

$\boxed{\bf{Perimeter=2(length + breadth ) }}$

A/q

$\mapsto\tt{2(r+m) = 240}\\\\\mapsto\tt{r+m=\cancel{240/2}}\\\\\mapsto\tt{r+m=120}\\\\\mapsto\tt{r=120-m.................(1)}$

&

If length is decreased by 10%, we get new dimensions of rectangle .

$\mapsto\tt{r\times \dfrac{(100-decreased\%)}{100} }\\\\\\\mapsto\tt{r\times \dfrac{(100-10)}{100} }\\\\\\\mapsto\tt{r\times \dfrac{9\cancel{0}}{10\cancel{0}} }\\\\\\\mapsto\tt{ \dfrac{9r}{10}\:cm }$

If breadth is increased by 20%, we get new dimensions of rectangle .

$\mapsto\tt{m\times \dfrac{(100-increased\%)}{100} }\\\\\\\mapsto\tt{m\times \dfrac{(100+20)}{100} }\\\\\\\mapsto\tt{m\times \dfrac{12\cancel{0}}{10\cancel{0}} }\\\\\\\mapsto\tt{ \dfrac{12m}{10}\:cm }$

Now;

$\mapsto\tt{2(new\:length + new\:breadth) = 240}\\\\\\\mapsto\tt{2\bigg(\dfrac{9r}{10} + \dfrac{12m}{10} \bigg)=240}\\\\\\\mapsto\tt{2\bigg(\dfrac{9r+12m}{10}\bigg)=240}\\\\\\\mapsto\tt{\bigg(\dfrac{9r+12m}{10}\bigg)=\cancel{\dfrac{240}{2}} }\\\\\\\mapsto\tt{\bigg(\dfrac{9r+12m}{10}\bigg)=120}\\\\\mapsto\tt{9r+12m=1200\:\:\underbrace{\sf{cross-multiplication}}}\\\\\mapsto\tt{9(120-m) + 12m=1200\:\:[from(1)]}\\\\\mapsto\tt{1080-9m+12m = 1200}\\\\\mapsto\tt{1080 + 3m =1200}$

$\mapsto\tt{3m=1200 - 1080}\\\\\mapsto\tt{3m=120}\\\\\mapsto\tt{m=\cancel{120/3}}\\\\\mapsto\bf{m=40\:cm}$

∴ Putting the value of m in equation (1),we get;

$\mapsto\tt{r=120-40}\\\\\mapsto\bf{r=80\:cm}$

Thus;

• The length of the rectangle is r = 80 cm .

• The breadth of the rectangle is m = 40 cm .