Question
If the side of an equilateral triangle is decreased by 20% , its area is decreased by
Answer: Option A
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Let the sides be `x` cm and `(80% of x) cm = (4x)/(5) cm`
Then , initial area = ` sqrt(3)/4 x^2` ,
final area = `sqrt(3)/4 ((4x)/(5))^2 = (16sqrt(3)x^2)/(100)`
Decrease in area = `(sqrt(3)/(4) x^2 - (16sqrt(3))/(100) x^2) cm^2 = (9sqrt(3) x^2)/(100) cm^2`
`:.` Decrease % = `((9sqrt(3)x^2)/(100) xx (4)/(sqrt(3)x^2) xx 100)`% = 36%
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