# What is the perimeter of a triangle with corners at (1 ,4 ), (3 , 2 ), and (2 ,7 )?

Jul 24, 2016

Perimeter $= 11.18 u n i t s$

#### Explanation:

Using the distance formula, we can solve for the length of each side of the triangle and then find the sum of those three sides.

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

For the first side we will use the points $\left(1 , 4\right)$ and $\left(3 , 2\right)$

${x}_{1} = 1$
${y}_{1} = 4$
${x}_{2} = 3$
${y}_{2} = 2$

$d = \sqrt{{\left(3 - 1\right)}^{2} + {\left(2 - 4\right)}^{2}}$
$d = \sqrt{{\left(2\right)}^{2} + {\left(- 2\right)}^{2}}$
$d = \sqrt{4 + 4}$
$d = \sqrt{8}$
$d = 2 \sqrt{2}$

For the second side we will use the points $\left(3 , 2\right)$ and $\left(2 , 7\right)$

${x}_{1} = 3$
${y}_{1} = 2$
${x}_{2} = 2$
${y}_{2} = 7$

$d = \sqrt{{\left(2 - 3\right)}^{2} + {\left(7 - 2\right)}^{2}}$
$d = \sqrt{{\left(- 1\right)}^{2} + {\left(5\right)}^{2}}$
$d = \sqrt{1 + 25}$
$d = \sqrt{26}$

For the third side we will use the points $\left(2 , 7\right)$ and $\left(1 , 4\right)$

${x}_{1} = 2$
${y}_{1} = 7$
${x}_{2} = 1$
${y}_{2} = 4$

$d = \sqrt{{\left(1 - 2\right)}^{2} + {\left(4 - 7\right)}^{2}}$
$d = \sqrt{{\left(- 1\right)}^{2} + {\left(- 3\right)}^{2}}$
$d = \sqrt{1 + 9}$
$d = \sqrt{10}$

${1}^{s t} s i \mathrm{de} = 2 \sqrt{2}$ $= 2.82$
${2}^{n d} s i \mathrm{de} = \sqrt{26}$ $= 5.10$
${3}^{r d} s i \mathrm{de} = \sqrt{10}$ $= 3.16$

$2 \sqrt{2} + \sqrt{26} + \sqrt{10}$

$2.82 + 5.10 + 3.16 =$

Perimeter $= 11.18 u n i t s$