Question

If the increase in the side of a square is 4% then find the approximate percentage of increase in the area of the square.

Answer 1

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Answer 2

The approximate percentage of increase in the area of the square is 8 %.

• Let the side of a square be taken as x.

• Area of a square with side x = (x)² = x²

• Now, if the side of the square is increased by 4 %, then the new side of the sqaure would be,

x + 4 % of x

= x + ( 4 / 100 ) × x

= x + ( 4x / 100 )

= ( 100x + 4x ) / 100

= 104x / 100

= 26x / 25

• Since the side is increased, the area of the square, too, would be increased.

 Increased area of the square = ( New side )² = ( 26x / 25 )²

= 676x² / 625

• Increase in area of the square = Increased area - Original area

= ( 676x² / 625 ) - x²

= ( 676x² - 625x² ) / 625

= 51x² / 625

• Now, approximate increase in the percentage of square's area = [ Increase in area / Original area ] × 100 %

= [ ( 51x² / 625 ) / x² ] × 100 %

= [ (51x² / 625 ) × ( 1 / x² ) ] × 100 %

= [ ( 51 x² × 1 ) / ( 625 × x² ) ] × 100 %

= ( 51 / 625 ) × 100 %

= 0.0816 × 100 %

= 8.16 %

• The approximate value of a decimal number means the integer part of the number, rounded off to its closest value.

• 8.16 % can be rounded off as 8.2 %, which can be further rounded off to 8 %

 ∴The required approximate percentage of increase in the area is 8 %.