Question

the perimeter of the triangle formed (4, 3) , (5, 1) and (1, -5) is (in units)​

Answer 1

$\textbf{Given:}$

$\text{Points are (4,3),(5,1) and (1,-5)}$

$\textbf{To find:}$

$\text{Perimeter of the triangle formed by the given 3 points}$

$\textbf{Solution:}$

$\text{Let the given points be}\;A(4,3),B(5,1) and C(1,-5)$

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

$AB=\sqrt{(4-5)^2+(3-1)^2}$

$AB=\sqrt{(-1)^2+(2)^2}$

$AB=\sqrt{1+4}$

$AB=\sqrt{5}$

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

$BC=\sqrt{(5-1)^2+(1+5)^2}$

$BC=\sqrt{(4)^2+(6)^2}$

$BC=\sqrt{16+36}$

$BC=\sqrt{52}$

$BC=2\sqrt{13}$

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

$CA=\sqrt{(1-4)^2+(-5-3)^2}$

$CA=\sqrt{(-3)^2+(-8)^2}$

$CA=\sqrt{9+64}$

$CA=\sqrt{73}$

$\textbf{Perimeter of triangle ABC}$

$=AB+BC+CA$

$=\sqrt{5}+2\sqrt{13}+\sqrt{13}\;\text{units}$