Question

if each side of a triangle is doubled, then find the percentage increase in its area

Answer 1

Using Heron's formula,
$area = \sqrt{s(s - a)(s - b)(s - c)}$
If each side is doubled, the each term in the formula s, (s-a), (s-b), and (s-c) doubled. Since they are under square root, area becomes 4 times. i.e., area increases by 3 times.
Therefore, percentage increase in area is
300%