Theory question 103
DifferentiationA side of a rectangle is three times the other. If the perimeter increases by 2%, find the percentage increase in the area of the rectangle.
Show the model answer
Model answer
Sides x and 3x: perimeter 8x, area 3x².
A 2% increase in perimeter (same shape) makes each side 1.02 times as long.
New area = 3(1.02x)² = 1.0404 × 3x².
Percentage increase in area = 4.04%.
Explanation
Area scales as the square of the length factor.