Question 1003124
the circumference of one of the wheels = c meters.


the circumference of the other wheel = c + 20 meters.


since both wheels are measured in meters, then the product will be in square meters.


the product, however, is in square millimeters.


it needs to be converted to square meters.


since 1 square millimeter is equal to 1 square meter / 1,000,000, then 144300 square millimters is equal to 144300 square millimmeters / 1,000,000 = .1443 square meters.


you get c * (c + 20) = .1443 square meters.


simplify to get c^2 + 20c = .1443 square meters.


subtract .1443 from both sides of the equation to get:


c^2 + 20c - .1443 = 0


solve this quadratic to get:


c = -20.0072124 meters or c = .0072124 meters


since c can't be negative, c must be equal to .0072124 meters


if c = .0072124 meters, then c + 20 = 20.0072124 meters


.0072124 meters * 20.0072124 meters = .1443 square meters.


this agrees with what the product should be, so c must be a good solution.


if you wanted to convert everything back to millimeters and square millimeters, you would then do the following.


.0072124 meters * 1000 = 7.2124 millimeters.


.0072124 meters * 1000 = 20007.2124 millimeters.


7.2124 millimeters * 20007.2124 millimeters = 144300.0187 square millimeters.


the difference between that and 144300 square millimeters is in the rounding.


what's shown as .0072124 meters is really 0.0072123990649864 meters rounded to 7 decimal digits.


if you use the numbers before they were rounded, you should get much closer to 144300.


i did and i got 144300 exactly.


if you have the capability, the recommendation is alwsys to use the unrounded numbers for all intermediate operations and then round for the final result only.