Question

9. Why is it not possible to make a right triangle using

lengths of 4 feet, 8 feet, and 10 feet? (2 pts)
A 4+8 is greater than 10.
B
10-8 does not equal 4.
C
42+82 does not equal 10².

Answer 1

C. 4² +8² ≠ 10²

Explanation:

You want to know why it is not possible for the lengths 4, 8, and 10 to form a right triangle.

Pythagorean theorem

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.