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

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

= 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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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.3 | Q 10 | Page 24

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