Question

If the sides of a triangle are doubled, then its area

• A. Remains the same
• B. Becomes doubled
• C. Becomes three times
• D. Becomes four times

Answer 1

The correct option is D Becomes four times

Using Heron's formula i.e.
$A=\sqrt{s(s-a)(s-b)(s-c)}$
where,
$s=\frac{a+b+c}{2}$
Let, $a_1=2a,b_1=2b,c_1=2c$
$\Rightarrow s_1=2s$
$\therefore A_1=\sqrt{2s(2s-2a)(2s-2b)(2s-2c)}$

taking 2 as common

$\therefore A_1=\sqrt{16s(s-a)(s-b)(s-c)}$
$\therefore A_1=4A$