the length of a rectangle exceeds its width by 5 M if the width is increased by 1 M and length is decreased by 2m area of a new rectangle is 4 square metres less than the area of the original rectangle . find the dimension of the original rectangle
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Let the width be x metres
Length = x + 5 metres
Area of the original rectangle = length × breadth
= (x + 5)(x)
= x² + 5x metres ______(i)
Given,
If the width is increased by 1 M and length is decreased by 2m,
the new dimensions will be ,
width = x + 1 metres
length = x + 5 - 2 = x + 3 metres
Area of the new rectangle will be
(x + 3)(x) = x² + 3x metres ______(i)
Given,
area of a new rectangle is 4 square metres less than the area of the original rectangle .
So,
a balanced equation can be formed like this :
Cancelling +x² and -x²,
we have,
x = 2
So,
Length = x + 5 m = 2 + 5m = 7m
Breadth = x = 2m
Thus,
the length and breadth of the rectangle will be 7m and 2m respectively
Let the width be x metres
Length = x + 5 metres
Area of the original rectangle = length × breadth
= (x + 5)(x)
= x² + 5x metres ______(i)
Given,
If the width is increased by 1 M and length is decreased by 2m,
the new dimensions will be ,
width = x + 1 metres
length = x + 5 - 2 = x + 3 metres
Area of the new rectangle will be
(x + 3)(x) = x² + 3x metres ______(i)
Given,
area of a new rectangle is 4 square metres less than the area of the original rectangle .
So,
a balanced equation can be formed like this :
Cancelling +x² and -x²,
we have,
x = 2
So,
Length = x + 5 m = 2 + 5m = 7m
Breadth = x = 2m
Thus,
the length and breadth of the rectangle will be 7m and 2m respectively
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