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:

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