Question

the perimeter of the rectangle is 240m .if its length is increased by 10 percentage and breadth is decreased by 20% we get the sam perimeter. Find the length and the breadth of the rectangle​

Answer 1

Given

Perimeter of rectangle = 240 m.

If length is increased by 10% & breadth is decreased by 20%,perimeter remains same.

To find

Length & breadth of rectangle

Solution

Let the length of rectangle be l m & breadth of rectangle be b m.

We know that,

➥ Perimeter of rectangle = 2(l + b)

Putting values we get :

⟼ 2(l + b) = 240

⟼ l + b = 240/2

⟼ l + b = 120 ..(1)

According to 2nd case :

➺ 2(l + 10% of l + b - 20% of b) = 240

➺ ( l + l/10 + b - b/5) = 240/2

➺ (11l/10 + 4b/5) = 120

➺ (11l + 8b)/10 = 120

➺ 11l + 8b = 120 × 10

➺ 11l + 8b = 1200 ..(2)

Now multiplying (1) into 11 and substract (2) from (1) :

11l + 11b = 1320 ..(3)

11l + 8b = 1200

(-) (-) (-)

⇒ 3b = 120

⇒ b = 120/3

⇒ b = 40

So, breadth of rectangle = 40 m.

Now putting this value in (1)

⇾ l + 40 = 120

⇾ l = 120 - 40

⇾ l = 80

So, length of rectangle = 80 m.

Therefore,

Length & breadth of rectangle are 80 m & 40 m respectively.

Answer 2

Answer:

Step-by-step explanation:

Solution:-

Let the length and breadth of the rectangle be x m and y m.

According to the Question,

⇒ x + y = 120 .... (i)

Length = x(100 - 10)/100

= 9x/10

Breadth = y(100 +20)/100

= 12y/10

Perimeter of rectangle = 240 m

2(L + B) = 240

⇒ 2(9x /10 + 12y /10) = 240

⇒  9x + 12y = 1200

⇒ 3x + 4y = 400 .... (ii)

Solving Eq (i) and (ii), we get

⇒ y = 40

Putting y's value in Eq (i), we get

⇒ x + y = 120

⇒ x + 40 = 120

⇒ x = 120 - 40

⇒ x = 80

Length = x = 80 m

Breadth = y = 40 m

Hence, the length and the breadth of the rectangle​ are 40 m and 80 m.