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

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.

Solution :

Let the length of rectangle be l and breadth be b

Given ; perimeter of a rectangle = 240 cm

$\sf \implies2(l + b) = 240$

$\sf \implies(l + b) = 120$

$\sf \implies \: l = 120 - b...(1)$

According to the question:

•Length is increased by 10%

⇒ New length ,l' = l+ 10% l = 1.1 l

• Breadth is decreased by 20%

⇒New breadth ,b' = b-20%b = 0.8 b

Now , New perimeter of reactangle

= 2(l' + b')

= 2 (1.1 l + 0.8 b ) ...(2)

But according to question,

initial perimeter of rectangle = final perimeter of rectangle

$\sf240 = 2(1.1l + 0.8b)$

$\sf \implies 1.1l + 0.8b = 120...(2)$

Now put l = 120- b in equation (2)

$\sf \implies1.1(120 - b) + 0.8b = 120$

$\sf \implies \frac{11(120 - b)}{10} + \frac{8b}{10} = 120$

$\sf \implies11(120 - b) + 8b = 1200$

$\sf \implies1320 - 11b + 8b = 1200$

$\sf \implies3b = 120$

$\sf \implies \: b \: = 40$

Now breadth of rectangle ,b = 40 cm

length , l = 120- b = 120-40 =80 cm

________________________

Verification:

l = 80 cm

b = 40 cm

perimeter

= 2(l+b)

= 2(80+40)

= 240

Hence verified!

Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

Let the dimensions of the rectangle are

• Length = x cm
• Breadth = y cm

Given perimeter = 240 cm

➠ 2(x + y) = 240

➠ x + y = 120 ……(i)

If the length is decreased by 10% and breadth is increased by 20% then the new dimensions are

Length = x × 100 - 10/100

= 90x/100

= 9x/10

Breadth = y × 100 + 20/100

= 120y/100

= 12y/10

Perimeter = 240 Cm

2(9x/10 + 12y/10) = 240

9x + 12y = 1200

Divide each term with 3.

➠ 3x + 4y = 400 ……(ii)

Multiply equation (i) with 3 and subtract from (ii)

• y = 40

Put y = 40 in (i)

x = 80

ThereFore,

Required length and breadth of the rectangle are:

• Length = x = 80 cm
• Breadth = y = 40 cm

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