Question

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

Answer 1

Answer:

I hope this will help you

where I have written equation 1 it is 1st part

Step-by-step explanation:

Perimeter of the rectangle given = 240cm

Let x cm be the length of the rectangle,

Let y cm be the breadth of the rectangle,

Answer 2

Step-by-step explanation:

Given:-

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

To Find:-

The length and breadth

Solution:-

$\bigstar \red{ \rm \:Let }$

• Length and breadth be x and y respectively.

$♠ \: \rm \: Perimeter \: of \: given \: rectangle = 240 \: cm$

$\rm \: Formula \: of \: perimeter \: of \: rect. \\ \longrightarrow \boxed{ \pink{ \tt \: 2(length + breadth)}}$

$\tt \: and \\ \rm \: 2(l + b) = 240 \\ \rm \dashrightarrow \: 2(x + y) = 240 \\ \rm \dashrightarrow \: x + y = \frac{240}{2} \\ \rm \dashrightarrow \: x + y = \frac{ \cancel{240}}{ \cancel {2}} - - - (i)$

$\rm \: Now \\ \\ \rm \: \bigstar \: New \: length = x - 10\% \: of \: x \\ \implies \rm \: x - \frac{x}{10} \\ \implies \rm \: \frac{10x - x}{10} \\ \implies \rm \: \frac{9x}{10} \\ \\ \rm \: \bigstar \: New \: breadth = y + 20\% \: of \: y \\ \implies \rm \: y + \frac{y}{5 } \\ \implies \rm \: \frac{5y + y}{5} \\ \rm \implies \frac{6y}{5}$

Now, given is that that the perimeter of New length and breadth is equal to the original perimeter, so

$\rm 2(length + breadth) = 240 \\\rm \longrightarrow2 \bigg( \: \frac{9x}{10} + \frac{6y}{5} \bigg) = 240 \\ \rm \longrightarrow \: \frac{9x}{10} + \frac{6y}{5} = \cancel{ \frac{240}{2} } \\ \rm \longrightarrow \frac{9x + 12y}{10} = 120 \\ \rm \longrightarrow9x + 12y = 120 \times 10 = 1200 - - - (ii)$

Multiplying (i) by 9 and then subtracting it from (ii)

$\rm \: 9(x + y = 120) \\ \rm \leadsto \: 9x + 9y = 1080 \\ \\ \rm \: 9x + 12y = 1200 \\ \rm \: 9x + 9y = 1080 \\ - \: \: \: - \: \: \: \: \: \: \: \: \: - \\ \rm \: - - - - - - - - - - \\ \rm \: 3y = 120 \\ \rm \: y = \cancel{\frac{ 120}{3} } \\ \rm \red{\boxed{ \rm \: y = 40 \: m}} \\ \\ \rm \: Putting \: y \: in \: (i) \: equation \\ \\ \rm \: x + y = 120 \: \\ \implies \rm \: x + 40 = 120 \\ \implies \: \rm \: x = 120 - 40 \\ \implies \red{ \boxed{ \rm \: 80 \: m}}$

So,

Length = 80 m

Breadth = 40 m