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Question
If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?
Solution
Area of an equilateral triangle having each side a cm is given by
`A = sqrt(3a^2)/a`
Now, Area of an equilateral triangle, say A1 if each side is tripled is given by
a = 3a
`A_1 = sqrt(3)/4a^2`
`A_1 = sqrt(3)/4(3a)^2`
`A_1 = (9sqrt(3)a^2)/4 cm ^2`
Therefore, increase in area of triangle
= A1-A
`=(9sqrt(3a^2))/4 - sqrt(3a^2)/4`
`= (8sqrt(3a^2))/4`
Percentage increase in area
`(8sqrt(3a^2)/4)/(sqrt(3a^2)/4) xx 100`
= 800%
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