If Each Side of a Equilateral Triangle is Tripled Then What is the Percentage Increase in the Area of the Triangle? - Mathematics

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Answer in Brief

If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?

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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

= 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%


Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
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RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.3 | Q 10 | Page 24

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