Question

Given √17, which side lengths are the legs of a special right triangle (e.g., 45-45-90 or 30-60-90)?

A) 4, 8
B) 1, 4
C) 1, 8
D) 2, 2

Answer 1

√17 cannot be the length of the legs of a special right triangle.

Step-by-step explanation:

To determine which side lengths are the legs of a special right triangle, we need to see if the given value of √17 can be expressed as a simplified radical. We can rewrite the value of √17 as a quotient of two integers since 17 is not a perfect square. Therefore, √17 cannot be the length of the legs of a special right triangle with integer side lengths like 45-45-90 or 30-60-90.

So, none of the given answer choices (A) 4, 8, (B) 1, 4, (C) 1, 8, or (D) 2, 2 are the correct side lengths of a special right triangle.