A rectangle is 14cm long and 10cm wide. if the length is reduced by x cms and its width is increased also by x cms so as to make it a square. find the change in the area.
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Length of rectangle = 14 cm
Width of rectangle = 10 cm
Area of rectangle = 140 cm²
Length of rectangle after it is reduced by 'x' cm = 14 - x cm
Width of rectangle after it is increased by 'x' cm = 10 + x cm
The rectangle is now a square as given in the problem statement, thus :-
Thus each side is of equal length,
Thus length = breadth
14 - x = 10 + x
-2 x = - 4
Thus, x=2
Substitute x= 2 in 14 - x OR 10 + x
Each side of the square is 12 cm long
Thus area of the square is 144 cm²
Change in area is = 144 - 140 = 4 cm²
Width of rectangle = 10 cm
Area of rectangle = 140 cm²
Length of rectangle after it is reduced by 'x' cm = 14 - x cm
Width of rectangle after it is increased by 'x' cm = 10 + x cm
The rectangle is now a square as given in the problem statement, thus :-
Thus each side is of equal length,
Thus length = breadth
14 - x = 10 + x
-2 x = - 4
Thus, x=2
Substitute x= 2 in 14 - x OR 10 + x
Each side of the square is 12 cm long
Thus area of the square is 144 cm²
Change in area is = 144 - 140 = 4 cm²
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