# What is the perimeter of a triangle with corners at (3 ,4 ), (2 ,0 ), and (4 ,9 )?

Perimeter $P = \sqrt{17} + \sqrt{26} + \sqrt{85} = 18.441669 \text{ }$units

#### Explanation:

Compute the distances from point to point
${d}_{1} = \sqrt{{\left(3 - 2\right)}^{2} + {\left(4 - 0\right)}^{2}} = \sqrt{1 + 16} = \sqrt{17}$
${d}_{2} = \sqrt{{\left(4 - 3\right)}^{2} + {\left(9 - 4\right)}^{2}} = \sqrt{1 + 25} = \sqrt{26}$
${d}_{3} = \sqrt{{\left(4 - 2\right)}^{2} + {\left(9 - 0\right)}^{2}} = \sqrt{4 + 81} = \sqrt{85}$

Perimeter is the sum$= {d}_{1} + {d}_{2} + {d}_{3} = \sqrt{17} + \sqrt{26} + \sqrt{85} = 18.441669 \text{ }$units

God bless....I hope the explanation is useful.