if the increase in the side of a square is 4% find the percentage of increase in the area of the square
Answers
Answer:
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 %.
Step-by-step explanation:
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