Question

If the sides of triangle are doubled then is area

• A. remains the same
• B. becomes doubled
• C. becomes three times
• D. become four times

Answer 1

Answer: (D)

become four times

Let the sides of triangle is a,b,c

Then area of triangle =$\sqrt{s(s-a)(s-b)(s-c)}$ where s=$\frac{1}{2}(a+b+c)$

If sides are doubled the new sides 2a,2b,2c

Then S=$\frac{1}{2}(2a+2b+2c)\Rightarrow 2\times \frac{1}{2}(a+b+c)=2s$

Then area of new triangle =$\sqrt{S(S-2a)(S-2b)(S-2c)}= \sqrt{2s(2s-2a)(2s-2b)(2s-2c)}=\sqrt{16}s(s-a)(s-b)(s-c)= 4\sqrt{s(s-a)(s-b)(s-c)}

Then area of new triangle =4 times of old triangle