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

Q: If every side of a triangle is doubled, then increase in the area of the triangle is:

$\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2},\text{A}=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$ Now, if $a' = 2a, b' = 2b$ and $c' = 2c$ Then, $\text{s}'=\frac{\text{a}'+\text{b}'+c'}{2}=\frac{2\text{a}+2\text{b}+2\text{c}}{2}=2\text{s}$ $\text{A}'=\sqrt{\text{s}'(\text{s},-\text{a}')(\text{s}'-\text{b}')(\text{s}'-\text{c}')}$ $=\sqrt{2\text{s}(2\text{s}-2\text{a})(2\text{s}-2\text{b})(2\text{s}-2\text{c})}$ $=4\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$ $\Rightarrow\text{A}' = 4\text{A}$ ⇒ Increase in Area $=\frac{4\text{A}-\text{A}}{\text{A}}\times100\%=300\%$ Hence, correct optin is $(c)$.

M.C.Q

GSEB - English Medium

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$400\%$

STD 9
Maths
Herons Formula
RD Sharma

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