Question

3. Use Structure When you are given three
side lengths for a triangle, how do you know
which length to substitute for a, b, or c in the
Pythagorean Th

Answer 1

Pythagorean Theorem a^2 + b^2 = c^2 applies only to right triangles, and c must be the hypotenuse (the side opposite the right angle). So when you are given three side lengths:

1. Identify the longest side — that is the candidate for c (the hypotenuse).
2. Put the other two sides as a and b (order of a and b doesn’t matter).
3. Check: if a^2 + b^2 = c^2 exactly, the triangle is right and your assignment is correct. If not, the triangle is not right and the Pythagorean Theorem does not hold.

Examples:
- Sides 5, 12, 13 → 13 is longest so c = 13. Check: 5^2 + 12^2 = 25 + 144 = 169 = 13^2 → right triangle.
- Sides 2, 3, 4 → 4 is longest so c = 4. Check: 2^2 + 3^2 = 4 + 9 = 13 ≠ 16 = 4^2 → not a right triangle.