the perimeter of a triangle is 0.097m and two of its sides measure 0.21dm and 42mm. determine the measurement of the third side in units of si, cgs and fps

1. Convert sides to the same unit (meters - SI):
l_1 = 0.21dm = 0.021m
l_2 = 42mm = 0.042m

2. Use the perimeter formula to find the third side:
P = l_1 + l_2 + l_3
0.097m = 0.021m + 0.042m + l_3
l_3 = 0.097m - 0.021m - 0.042m
l_3 = 0.034m

3. Convert to CGS units (centimeter-gram-second):
l_3 = 0.034m \times 100cm/m = 5.5cm

4. Convert to FPS units (foot-pound-second):
l_3 = 0.034m \times \frac{3.28084ft}{1m} \approx \frac{11}{200} ft

Answer:
l_3 = 0.034m (SI)
l_3 = 3.4cm (CGS)
l_3 = \frac{11}{200} ft (FPS)