In a painting competition of a school a child made lndian flag whose perimeter was 50cm.lts area will be decreased by 6square cm, if length is decreased by 3cm and breadth is increased by 2cm, then find the dimensions of the flag?

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Solution

Let the dimensions of the flag be l x b where l = length in cm and b = breadth in cm,
Perimeter of rectangle = 2l+2b = 50cm (given) (1)
Area A= lb sq cm
If we decrease length by 3cm and increase breadth by 2cm, A is decreased by 6 sq cm. This can be expressed by the equation:
(l-3)(b+2)= lb-6
or lb-3b+2l-6=lb-6
or 3b = 2l
or b= 2l/3
Substituting into equation (1) we get
2l+2(2l/3)= 50
2l+4l/3= 50
$\frac{6 l + 4 l}{3}$ = 50
10l/3 = 50
l = 50(3/10) = 15cm
b = 2l/3= 2/3(15) = 10cm
Answer: Length = 15cm and breadth = 10 cm

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