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According to the geometry program used to draw the triangle, the lengths of the sides add to 21.841 units*. Rounded to the nearest tenth, the appropriate answer choice is ...
... 21.8
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You can use your test-taking skill to choose this answer without doing a single calculation. The answer choices appear to be about rounding, not about accurate calculation of the length. The choice 21.84 tells you that is probably the value before any rounding. Then choices 22 and 21.9 are obviously incorrectly rounded. The correctly rounded answer is then 21.8.
Coordinate differences are ...
AB = (-1, 6) -(-4, 0) = (3, 6) . . . . ║AB║=√(3²+6²)=3√5
BC = (3, -1) -(-1, 6) = (4, -7) . . . . ║BC║=√(4²+7²)=√65
CA = (-4, 0) -(3, -1) = (-7, 1) . . . . ║CA║=√(7²+1²)=5√2
The sum of these lengths is about 21.8415, so rounds to 21.8.
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* If you follow the math, you find that the final sum should be displayed using 3 decimal digits as 21.842. The error in the least-significant digit of the sum comes from rounding each length to 3 decimal digits.
