# What is the perimeter of a triangle with corners at (7 ,3 ), (8 ,5 ), and (3 ,4 )?

Jan 18, 2018

Perimeter ${P}_{t} = \left(a + b + c\right) = 5.099 + 4.1231 + 2.2361 = \textcolor{p u r p \le}{11.5831}$

#### Explanation:

Perimeter of triangle ${P}_{t} = a + b + c$ where a, b, c are the lengths of the three sides.

a is equal to distance between points B & C

Distance formula given the coordinates of two points is

$d = \sqrt{{\left(x 2 - x 1\right)}^{2} + {\left(y 2 - y 1\right)}^{2}}$

$a = \sqrt{{\left(3 - 8\right)}^{2} + {\left(4 - 5\right)}^{2}} = 5.099$

$b = \sqrt{{\left(7 - 3\right)}^{2} + {\left(3 - 4\right)}^{2}} = 4.1231$

c = sqrt((8-7^2 + (5-3)^2) = 2.2361

Perimeter ${P}_{t} = \left(a + b + c\right) = 5.099 + 4.1231 + 2.2361 = \textcolor{p u r p \le}{11.5831}$