Question

In a painting competition of a school a child made Indian national flag whose perimeter was 50 cm . It's area will be decreased by 6square cm if length is decreased by 3 cm and breadth is increased by 2 cm . Find the dimensions of flag

Answer 1

2(l+b)=50 

2l+2b=50

l-3(b+2)=lb-6

lb+2l-3b-6=lb-6

2l-3b=0

2l+2b=50

-   -      -

     -5b=-50

b=10

2l+20=50

2l=30

l=15

Answer 2

Answer:

The dimensions, length and breadth of the flag is 15 cm and 10 cm respectively.

Solution:

The shape of the Indian National Flag is a rectangle.

Let the flag made by the child have a length l and breadth b.

Given, Perimeter of the flag = 50 cm

We know, Perimeter of a rectangle = 2 (length + breadth)

So,

$\begin{array} { l } { 2 ( 1 + b ) = 50 \mathrm { cm } } \\\\ { l + b = \frac { 50 } { 2 } c m } \\\\ { l + b = 25 \mathrm { cm } } \\\\ { l = 25 - b \mathrm { cm } \ldots \ldots \text { (i) } } \end{array}$

And, Area of the flag will be = l x b = lb

Given, when length becomes (l-3) cm

And, breadth becomes (b+2) cm,

Area becomes decreased by $6 cm^2$,

i.e. $Area = (lb-6) cm^2$

$( l - 3 ) ( b + 2 ) = ( l b - 6 )$

Putting l = 25-b cm from (i) in the above equation, we get,

$\begin{array} { c } { ( 25 - b - 3 ) ( b + 2 ) = ( ( 25 - b ) b - 6 ) } \\\\ { ( 22 - b ) ( b + 2 ) = \left( 25 b - b ^ { 2 } - 6 \right) } \\\\ { 22 b - b ^ { 2 } + 44 - 2 b = 25 b - b ^ { 2 } - 6 } \\\\ { 20 b - b ^ { 2 } + 44 = 25 b - b ^ { 2 } - 6 } \end{array}$

$\begin{array} { c } { 44 + 6 = 25 b - 20 b } \\\\ { 5 b = 50 } \\\\ { b = \frac { 50 } { 5 } } \\\\ { b = 10 } \end{array}$

And      

$\begin{array} { c } { l = 25 - b c m } \\\\ { l = 25 - 10 c m = 15 \mathrm { cm } } \end{array}$

Thus, the dimensions, length and breadth of the flag is 15 cm and 10 cm respectively.