Question
Download Solution PDFIf each side of a square be increased by 10%, the percentage increase in area is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Side of a square increased = 10%
Formula used:
Increase = New number - Original number
% increase = (Increase/Original Number) × 100
Area of square = side2
Calculations:
Let the side of the square be a
Area of a square with side a = a2
After increasing percentage of side a by 10% = a + 10% of a
⇒ a(1 + 10/100) = a(1 + 1/10)
⇒ a(11/10) = 11a/10
Area of the square after increasing side by a = (11a/10)2
⇒ (11a/10) × (11a/10) = 121a2/100
⇒ 1.21a2
Percentage change in area of square =[(1.21a2 - a2)/a2] × 100
⇒ [a2(1.21 - 1)/a2] × 100 = 0.21 × 100
⇒ 21%
∴ Percentage change in area of square is 21%
Alternate Method
Percentage increase in a regular polygon = x + y + (xy/100)
In square length and breadth are same, x = y
Percentage increase = x + x + (xx/100)
⇒ 2x + x2/100 = 2 × 10 + 10 × 10/100
⇒ 20 + 1 = 21%
∴ The required percentage is 21%
Last updated on Jun 21, 2023
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