What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? 19.2 units 22.3 units 27.4 units 36.0 units

A geometry app shows lengths that add up to 27.4 units.

The Pythagorean theorem can be used to find the lengths of the segments. Each length is the square root of the sum of squares of the difference in x-coordinates and the difference in y-coordinates.

segment AB: length = √(3²+8²) = √73 ≈ 8.544

segment BC: length = √(7²+4²) = √65 ≈ 8.062

segment CA: length = √(10²+4²) = √116 ≈ 10.770

Then the total perimeter is the sum of these lengths:

... 8.544 +8.062 +10.770 = 27.376 ≈ 27.4 . . . . units

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: