Answer:
42.668 mm to 42.672 mm.
Step-by-step explanation:
According to given situation, Production will be stopped if the discrepancy in diameter is greater than 0.002 mm.
The difference in the limits are,
42.67 - 0.002 = 42.668
42.67 + 0.002 = 42.672
Therefore, the range of acceptable values are 42.668 mm to 42.672 mm
0.002 larger than 42.67 mm, or a diameter more than 0.002 smaller than 42.67. This is the reason for using an absolute value function.
Absolute value represents the distance a number is from 0. For this function, we would want only the values where the function is less than 0.002.
Let x represent the length of the shorter leg.
Longer leg: 5x +19
Hypotenuse: 5x +20
Pythagorean theorem:
.. x^2 +(5x +19)^2 = (5x +20)^2
.. x^2 +25x^2 +190x +19^2 = 25x^2 +200x +20^2 . . . . . . eliminate parentheses
.. x^2 -10x -39 = 0
.. (x -13)(x +3) = 0
.. x = 13 . . . . . . . . . . leg lengths must be positive
The side length of the triangle are 13, 84, 85 feet.