Hey there!!
Basic formula :
Area of a rectangle = Length × breadth
Given :
Width = two third of the length
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Let's take the dimension of the length as ' x '
Then the breadth would be = 2x / 3
Area = ( x ) × ( 2x / 3 )
Area = 2x² / 3
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Each dimension is decreased by 2
This states that we will need to add 2 to both length and breadth
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Length = x - 2
Breadth = 2x / 3 - 2
= 2x - 6 / 3
Area = ( x - 2 ) × ( 2x - 6 / 3 )
Area = 2x² - 10x + 12 / 3
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What they say?
Area is decreased by 32 cm
Which means..
If we add 32 to the new rectangles area , the areas would be equal to the new and the old rectangle
2x² / 3 = ( 2x² - 10x + 12 / 3 ) + ( 32 )
2x² / 3 = 2x² - 10x + 108 / 3
Multiplying by 3 on both sides
2x² = 2x² - 10x + 108
Adding 10x on both sides
2x² + 10x = 2x² + 108
subtracting by 2x² on both sides
10x = 108
Dividing by 10 on bot sides
x = 10.8
Length of the original rectangle = 10.8 cm
Breadth = 2 ( 10.8 ) / 3
= 7.2 cm
Hope my answer helps!
