Question

If the sides of a triangle are doubled, which of the following will be true about its area?

• A. remians same
• B. is doubled
• C. becomes 4 times
• D. inadequate data
• E. none of these

Answer 1

The correct option is C becomes 4 times

Let, the original sides be a,b and c.
$s=\frac{1}{2}(a+b+c)$
and area of the triangle =$\sqrt{s(s-a)(s-b)(s-c)}$
For the new triangle, the sides are 2a, 2b, 2c.
Then, $S=\frac{1}{2}(2a+2b+2c)=a+b+c=2s.$
$\therefore$ Area of new triangle
$=\sqrt{S(S-2a)(S-2b)(S-2c)}=\sqrt{2s(2s-2a)(2s-2b)(2s-2c)}=\sqrt{16s(s-a)(s-b)(s-c)}=4\sqrt{s(s-a)(s-b)(s-c)}$
$=4\times$ (area of original triangle)