# How do you find the perimeter of a triangle given (2, 2), (-2, 2), and (-2, -3)?

Apr 21, 2018

Perimeter is $15.4$

#### Explanation:

To find perimeter, we should find sum of all the three sides of the triangle formed by $A \left(2 , 2\right)$, $B \left(- 2 , 2\right)$ and $C \left(- 2 , - 3\right)$

Before we do that observe that between $A$ and $B$, ordinate is same and hence line joining them is parallel to $x$-axis. Further as difference between abscissa is $4$, length of $A B$ is $4$.

Also observe that between $B$ and $C$, abscissa is same and hence line joining them is parallel to $y$-axis. Further as difference between ordinate is $5$, length of $B C$ is $5$.

As $A B$ is parallel to $x$-axis and $B C$ is parallel to $y$-axis, $\Delta A B C$ is right angled triangle and hence from Pythagoras theorem, hypotenuse $A C = \sqrt{{4}^{2} + {5}^{2}} = \sqrt{16 + 25} = \sqrt{41} = 6.403 \cong 6.4$

and perimeter is $4 + 5 + 6.4 = 15.4$