Question

the length of a rectangle exceeds its breadth by 7 cm is the length is decreased by 4 centimetre and breadth is increased by 3 cm in the area of a new rectangle is same to the area of the original rectangle

Answer 1

Let Breath=X cm
Then Length exceed 7 cm=(X+7)cm

Now Breath exceed by 3 =(X+3)cm
Now Length decrease by 4=(x+7-4)=(x+3)cm

Area = Length×breath
Question says both rectangle area is same
THEN a/q
x×(x+7)=(x+3)×(x+3)
x²+7x=x²+3x+3x+9
x²+7x-x²-3x-3x=9
7x-6x=9
x=9
So Breath is =9cm
Length=9+7=16cm

another rectangle Length =12cm
Breath=12cm

Answer 2

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$Let\:the\:breadth\:of\:rectangle\:is\:'x'\:cm\\\\and\:the\:length\:of\:rectangle\:is\:x+7\\\\Area=x(x+7)\\\\\\According\:to\:the\:question,\\\\\\(x+7-4)\:(x+3)=x\:(x+7)\\\\\\\implies(x+3)\:(x+3)=x^2+7x\\\\\implies(x+3)^2=x^2+7\\\\\implies x^2+9+6x=x^2+7x\:(Here\:'x^2'\:and'x^2'\:are\:cancelled)\\\\\implies6x-7x=-9\\\\\implies-x=-9\:(here\:'-'\:and\:'-'\:are\:cancelled)\\\\\implies x=9\\\\\\Length=x+7=9+7=\boxed{16\:answer}\\\\Breadth=\boxed{x=9\:answer}$