Question

if the side of an equilateral triangle are tripled then find its area using herons formula​

Answer 1

Answer:

let the initial side be 'a'

semi perimeter(s)= 3a/2

area = √s(s-a)(s-b)(s-c) [Herons formula]

= √3a/2(3a/2-a)(3a/2-a)(3a/2-a)

= √3a/2×a/2×a/2×a/2

= √3a^4/16

= √3/4a^2

now if the side is tripled,

new side = 3a

semi perimeter (s) = 9a/2

area= √s(s-a)(s-b)(s-c)

= √9a/2×3a/2×3a/2×3a/2

= 9√3/4 a^2

so new area becomes 9 times the original area.

hope it helps you

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