Answer:
C. 4² +8² ≠ 10²
Step-by-step explanation:
You want to know why it is not possible for the lengths 4, 8, and 10 to form a right triangle.
The side lengths of a right triangle must satisfy the Pythagorean relation:
a² +b² = c²
These numbers do not:
4² +8² = 16 +64 = 80 ≠ 10² = 100
A right triangle is not formed because ...
4² +8² ≠ 10²
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Additional comment
The smallest Pythagorean Triple is {3, 4, 5}. Doubling these numbers gives {6, 8, 10}. If the two longest sides are 8 and 10, the shortest must be 6 for a right triangle to be formed.
When the side lengths are reduced to a mutually prime set of numbers, their sum must be even.
4:8:10 reduces to 2:4:5 which has an odd sum.
