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Let one parallel be x+1.75 and the other parallel be x:

1/2(sum of parallels)height = area

1/2(x+1.75+x)16 = 174 cm2

Multiply both sides by 2 and then divide both sides by 16:

x+1.75+x = 21.75

Collect like terms and subtract 1.75 from both sides:

2x = 20 => x = 10

Therefore the lengths of the parallels are 11.75 cm and 10 cm

Check: 1/2(11.75+10)16 = 174 cm2

Q: How do you work out in detail the lengths of the parallels of a trapezoid when one base is 1.75 cm longer than the other and has a height of 16 cm with a square area of 174 cm?

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