Question

The length and breadth of a rectangle are in ratio 2:1. If the length is increased by 2 cm and breadth is increased by 3 cm, then the ratio
of the perimeter of the original rectangle to the perimeter of the new rectangle is 4:3. Find the dimensions of the original rectangle. NO IRRELEVANT ANSWERS, OTHERWISE I WILL REPORT

Answer 1

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Answer 2

Answer:

(CONTRARY)

Case i        ( 40/3 ) x ( 20/3 )

Case ii       ( 8/3 ) x ( 4/3 )

Case iii      ( 10 ) x ( 5 )

Step-by-step explanation:

Let the length be 'l' and the breadth be 'b'

Given

l : b = 2 : 1

Now Let the new length be 'L' and 'B'

Given

L = l + 2

B = b +3

Formula: Perimeter of a rectangle = 2 ( Length + Breadth)

Now

Perimeter of old rectangle say 'p' = 2 ( l + b )

Perimeter of new rectangle say 'P' = 2 ( L + B )

Given

p : P = 4 : 3

=> 2 ( l + b ) : 2 ( L + B ) = 4 : 3

=> ( l + b ) : ( L + B ) = 4 : 3

=> ( l + b ) : ( l + 2 + b +3 ) = 4 : 3

=> ( l +b ) : ( l + b + 5 ) = 4 : 3

$=>\frac{l+b}{l+b+5}=\frac{4}{3}\\\\=>3(l+b)=4(l+b+5)\\\\=>l+b=-20\\which\; is\; not \;possible\\\\Hence \;the\;given\;information\;is\;wrong$

Now

Three cases may arise

(i) length and breadth have been decreased instead of increment

(ii) breadth was decreased instead of increment

(iii) ratio 4:3 is P : p rather than p : P

Case i:

Length and breadth have been decreased then

L = l - 2

B = b - 3

P = 2 ( l + b - 5)

Now

p : P = 4 : 3

=>( l + b ) : ( l + b - 5 ) = 4 : 3

$=>\frac{l+b}{l+b-5}=\frac{4}{3}\\\\=>3(l+b)=4(l+b-5)\\\\=>l+b=20\\\\Given\\l:b=2:1\\\\=>\frac{l}{b}=2\\\\=>l=2b\\\\Sub\;above\\\\=>2b+b=20\\\\=>3b=20\\\\=>b=\frac{20}{3}\\\\=>l=\frac{40}{3}$

Hence in this case length = 40/3 m   breadth is 20/3 m

Case ii

Breadth was decreased instead of increment then

L = l + 2

B = b - 3

P = 2 ( l + b - 1 )

Now

p : P = 4 : 3

=>( l + b ) : ( l + b - 1 ) = 4 : 3

$\frac{l+b}{l+b-1}=\frac{4}{3}\\\\by\;observation\\\\l+b=4\\\\Now\; Since \;l=2b\\\\2b+b=4\\\\=>3b=4\\\\=>b=\frac{4}{3}\\\\=>l=\frac{8}{3}$

In this case length is 8/3 m breadth is 4/3 m

Case iii

P : p = 4 : 3

=> ( l + b + 5 ) : ( l + b ) = 4 : 3

$\frac{l+b+5}{l+b}=\frac{4}{3}\\\\=>3(l+b+5)=4(l+b)\\\\=>l+b=15\\\\Since\;\;l=2b\\substitute\; above\\\\=>2b +b = 15\\\\=>3b=15\\\\=>b=5\\\\=>l=10$

In this case the length is 10 m and the breadth is 5m

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