Question

△xpm is a right triangle where ( mangle xpm = 90^circ ), ( xp = 16 ), and ( xm = 20 ).
determine the length of ( mp ). if necessary, round your answer to the nearest thousandth.
3.
( \bigcirc ) 53.130
( \bigcirc ) 15.549
( \bigcirc ) 45.962
( \bigcirc ) 56.134
( \bigcirc ) 12
( \bigcirc ) 40
( \bigcirc ) 35
( \bigcirc ) 14.665
( \bigcirc ) 28.601
( \bigcirc ) 48.888
( \bigcirc ) 61.928
( \bigcirc ) 32.451
( \bigcirc ) 27
( \bigcirc ) 45
( \bigcirc ) 18
( \bigcirc ) 63.458

Explanation:

Step1: Identify right triangle sides

We have right triangle $\triangle XPM$ with $\angle XPM = 90^\circ$, so $XP=16$ (one leg), $XM=20$ (hypotenuse), and $MP$ is the unknown leg.

Step2: Apply Pythagorean theorem

The theorem states $a^2 + b^2 = c^2$, where $c$ is the hypotenuse. Rearrange to solve for $MP$:
$$MP = \sqrt{XM^2 - XP^2}$$

Step3: Substitute values and calculate

$$MP = \sqrt{20^2 - 16^2} = \sqrt{400 - 256} = \sqrt{144} = 12$$

Answer:

12