Question

If each side of a triangle is doubled then find the increased percent of the area of a triangle

Answer 1

$let \: the \: sides \: of \: triangle \: be \\ a \: \: \: b \: \: \: and \: \: \: c$
$then \: area \: is \: obtained \: using \\ \sqrt{s(s - a)(s - b)(s - c)} \\ where \: \: s = \frac{a + b + c}{2}$
$if \: the \: sides \: are \: doubled \\ s \: \: will \: double \\ (s - a) \: \: will \: double \\ (s - b) \: \: will \: double \\ (s - c) \: \: will \: double$
$thus \: area \: will \: be \: 4 \: times \: \\ i.e. \: percentage \: increase \: is \: 300\%$