Given two equilateral triangle; the length of the sides of the 2nd triangle are 2 less than 3 times the length of the sides of the 1st triangle. If the Perimeter of the 2nd triangle is 102
inches; Find the lengths of the sides of both triangles and the perimeter of the 1st triangle
to the nearest 10th of a milimeter (2.54 cm/inch; 10mm/cm)

9514 1404 393

  first triangle -- side: 304.8 mm; perimeter: 914.4 mm

  second triangle -- side: 863.6 mm; perimeter: 2590.8 mm

Step-by-step explanation:

We are given two equilateral triangles. The perimeter of the second is given as 102 inches, so its sides have length 102/3 = 34 inches. This is 2 less than 3 times the side length in the first triangle. So, adding 2 will give 3 times the side length of the first triangle: 36 inches, which also happens to be its perimeter. Those side lengths are 36/3 = 12 inches.

Now, we know:

  first triangle -- side length 12 inches, perimeter 36 inches

  second triangle -- side length 34 inches, perimeter 102 inches.

These measurements are desired in millimeters. Each inch is 25.4 millimeters, so we can find the desired measures by multiplying these numbers by 25.4.

  12×25.4 = 304.8; 36×25.4 = 914.4

  34×25.4 = 863.6; 102×25.4 = 2590.8

The desired lengths are ...

  first triangle -- side: 304.8 mm; perimeter: 914.4 mm

  second triangle -- side: 863.6 mm; perimeter: 2590.8 mm

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step-by-step explanation:

"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: