The length of a rectangular hall exceeds its breadth by 7 cm. If the breadth is decreased by 1m and the length increased by 2m the area remains the same.find the length and breadth of the hall

Asked by ajayrath7 | 11th Nov, 2017, 09:38: AM

Expert Answer:

Linear Equations in One Variable:
 
begin mathsize 16px style Let space the space breadh space of space rectangle space be space straight x space straight m.
rightwards double arrow length space of space straight a space rectangle equals left parenthesis straight x plus 7 right parenthesis space straight m
Thus comma space area space of space rectangle equals length space straight x space breadth equals straight x left parenthesis straight x plus 7 right parenthesis space straight m squared

For space new space rectangle.
breadh equals left parenthesis straight x minus 1 right parenthesis space straight m.
length equals left parenthesis straight x plus 7 plus 2 right parenthesis space straight m
Thus comma space area space of space new space rectangle equals length space straight x space breadth equals left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 7 plus 2 right parenthesis space straight m squared

Now comma
straight x left parenthesis straight x plus 7 right parenthesis equals left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 7 plus 2 right parenthesis
rightwards double arrow straight x squared plus 7 straight x equals left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 9 right parenthesis
rightwards double arrow straight x squared plus 7 straight x equals straight x squared plus 8 straight x minus 9
rightwards double arrow straight x equals 9 equals breadth
rightwards double arrow straight x plus 7 equals 9 plus 7 equals 16 equals length
end style

Answered by  | 8th Dec, 2017, 11:59: AM