Question

The perimeter of a triangle with vertices $(0,4),(0,0)\mathrm{and}(3,0)$ is ,

• A. $5$
• B. $12$
• C. $11$
• D. $7+\sqrt{5}$

Answer 1

The correct option is B

$12$

The explanation for the correct option.

The vertices of a triangle $ABC$ are $A(0,4),B(0,0)\mathrm{and}C(3,0)$.

The perimeter of $∆ABC=AB+BC+AC$

The distance between the points $(x_1,y_1)\mathrm{and}(x_2,y_2)$ is given by,

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$$\begin{gathered} \therefore P=AB+BC+AC \\ \Rightarrow \sqrt{{(0-0)}^2+{(0-4)}^2}+\sqrt{{(3-0)}^2+{(0-0)}^2}+\sqrt{{(3-0)}^2+{(0-4)}^2} \\ \Rightarrow \sqrt{16}+\sqrt{9}+\sqrt{9+16} \\ \Rightarrow 4+3+\sqrt{25} \\ \Rightarrow 7+5 \\ \Rightarrow 12 \end{gathered}$$

Hence, the option $B$is correct.