Question

If every side of a triangle is doubled then increase in the area of the triangle is--

• A. $100\sqrt{2}\%$
• B. $200\%$
• C. $300\%$
• D. $400\%$

Answer 1

The correct option is C $300\%$

Let the lengths of sides of any triangle be $a,b,c$ and its semi-perimeter be $s$ i.e. $s=\frac{a+b+c}{2}$ then
Area of the triangle is

$A=\sqrt{s(s-a)(s-b)(s-c)}$
Let's double each side of the same triangle, then

New semi-perimeter will be $S=\frac{2a+2b+2c}{2}=a+b+c=2s$
Thus, the new area of triangle
$=\sqrt{2s\cdot (2s-2a)(2s-2b)(2s-2c)}$
$=4\sqrt{s(s-a)(s-b)(s-c)}$
$=4A$
$\therefore$ Reqd. increase $\%$ in the area of $\Delta$

$=\frac{4A-A}{A}\times 100$%
= $300\%$