# For a given right triangle one side is 19cm and the other is 18cm. What is the missing measurement?

Apr 16, 2017

Assuming the two measurements are for the arm of the right triangle and the missing side is the hypotenuse - see the solution process below:

#### Explanation:

The Pythagorean Theorem states; For a right triangle:

${c}^{2} = {a}^{2} + {b}^{2}$; Where $a$ and $b$ are arms of the triangle and $c$ is the hypotenuse of the triangle.

Substituting the values from the problem and solving for $c$ gives:

${c}^{2} = {19}^{2} + {18}^{2}$

${c}^{2} = 361 + 324$

${c}^{2} = 685$

$\sqrt{{c}^{2}} = \sqrt{685}$

$c = \sqrt{685} c m = 26.173 c m$ rounded to the nearest thousand.

However, if the given sides are not the arms and it is the hypotenuse which is 19cm the results will be different as pointed out by @abdur-r.