Question

Example 16. The perimeter of a rectangle is 240 cm. If its length is decreased by 10% and breadth is
increased by 20%, we get the same perimeter. Find the length and the breadth of the rectangle.​

Answer 1

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Let ,

• Length » l
• Breadth » b

Condition :

• length is decreased by 10%

» ⟩ new length = l - l. (10 /100 )=( 10l -l)/10 = 9 l /10

• breadth is increased by 20%

»⟩. new breadth = b + b(20/100) = 6b/5

A/Q ,

2{(9l/10) +(6b/5)} = 240

=> 9l /10 + 6b/5. = 120

=> (9l+12b)/10 = 120

=> 9l + 12 b = 1200

=> 3l + 4b = 400 _______(1)

We are given ,

2 ( l+b)= 240

=> l+b = 120 ____________(2)

3 × eq. no. (2)

=> 3l+ 3b = 360 ________(3)

now ,

(1) -(2) => b= 40

so , breadth ~ 40cm.

Putting , the value of b in eq. no. (2)

l+40 =120

=> l = 80

so, Length ~ 80cm.

$\bold{\boxed{Length\:80cm.}}$

$\bold{\boxed{Breadth\:40cm.}}$