Question

The perimeter of a rectangle is 240cm.If the 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.

Answer 1

Given:

• A rectangle with perimeter 240 cm.

• Perimeter of given rectangle does not changes when length is increased by 10% and breadth is decreased by 20%

To Find:

• Length and breadth of the given rectangle

Solution:

We know that,

Perimeter of Rectangle= 2(Length×Breadth)

Let the length and breadth of the given rectangle be 'l' and 'b' respectively.

Now,

According to Question

⇒ 2(l+b)= 240

⇒ l+b= 120

⇒ l= 120-b --------------------(1)

Now,

After increasing the length by 10%

Final Length,l'= l+10% of l

$l'=l+\dfrac{10}{100}l$

$l'=l+\dfrac{l}{10}$

$l'=\dfrac{10l+l}{10}$

$l'=\dfrac{11l}{10}$

After decreasing the breadth by 20%

Final Breadth,b'= b-20% of b

$b'=b-\dfrac{20}{100}b$

$b'=b-\dfrac{2b}{10}$

$b'=\dfrac{10b-2b}{10}$

$b'=\dfrac{8b}{10}$

Now, According to the question

$\longrightarrow\sf{2(l'+b')=240}$

$\longrightarrow\sf{l'+b'=\dfrac{240}{2}}$

$\longrightarrow\sf{l'+b'=120}$

Now, after putting values of l' and b' in above equation, we get

$\longrightarrow\sf{\dfrac{11l}{10}+\dfrac{8b}{10}=120}$

$\longrightarrow\sf{\dfrac{11l+8b}{10}=120}$

$\longrightarrow\sf{11l+8b=120\times10}$

$\longrightarrow\sf{11l+8b=1200}$

From (1),

$\longrightarrow\sf{11(120-b)+8b=1200}$

$\longrightarrow\sf{1320-11b+8b=1200}$

$\longrightarrow\sf{-11b+8b=1200-1320}$

$\longrightarrow\sf{-3b=-120}$

$\longrightarrow\sf{3b=120}$

$\longrightarrow\sf{b=\dfrac{120}{3}}$

$\longrightarrow\sf{b=40cm}$

On putting value of b in (1), we get

✏ l= 120-40

✏ l= 80cm

Hence, length and breadth of the given rectangle are 80cm and 40 cm respectively.

Answer 2

Given :-

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

To Find :-

• The length and breadth of the rectangle. ?

Formula used :-

• Perimeter of Rectangle = 2(Length + Breadth) .

Solution :-

Let Length & Breadth of Rectangle are L & B Respectively.

A/q,

→ 2(L+B) = 240

→ L + B = 120 ------------------ Equation (1).

______________

Now, length is increased by 10% and its breadth is decreased by 20%.

So,

→ New Length = L + 10% of L = L + 0.1L = 1.1L

→ New Breadth = B - 20% of B = B - 0.2B = 0.8B

So,

→ 2(1.1L + 0.8B) = 240

→ 1.1L + 0.8B = 240 ---------------- Equation (2).

______________

From Both Equations we can say That ,

==>> Equation (1) = Equation (2) = 120

So,

→ L + B = 1.1L + 0.8B

→ B - 0.8B = 1.1L - L

→ 0.2B = 0.1L

→ B/L = 0.1/0.2

→ B/L = 1/2

Or,

→ B : L = 1 : 2

______________

So, New Lets Assume That, B is x cm & L is 2x cm.

→ 2(x + 2x) = 240

→ 3x = 120

→ x = 40.

Hence ,

→ Length = 2x = 2*40 = 80cm.

→ Breadth = x = 40cm.

Therefore , Length & Breadth of Rectangle are 80cm & 40cm Respectively.