Question

The side lengths of a triangle are 5, 8, and 12. Is this a right triangle?

O A. No, because 52 + 32 + 122.
OB. No, because 5+ 8 + 12.
C. Yes, because 52 + 82 = 122.
O D. Yes, because 52 + 82 < 122

Answer 1

A) No...

Explanation:

We can check if this triangle is a right triangle by using the Pythagorean Theorem.

• a² + b² = c²
• where a and b are the legs of the right triangle, and c is the hypotenuse (longest side)

Using 5 for a, 8 for b, and 12 for c, let's see if this satisfies the equation:

• 5² + 8² = 12²

Simplify.

• 25 + 64 = 144

• 89 = 144

We can see that 89 ≠ 144, so this leaves us with answer choices A and B. I think you meant to write < for the last + sign.

Seeing as the sum of the two lengths of the triangle is greater than the third side length, this creates a normal triangle. This cannot be the correct answer choice since this only satisfies the requirements for a triangle, but not a right triangle.

This leaves us with answer choice A. 52 + 32 ≠ 122 and 52 + 32 < 122. (I'm not sure why the squares of the side lengths are not used, but this should be the correct answer.)