Question

Given the two pairs of values, answer the following questions. Xq = 5, Y1 = 4, X2 = 1, y = 1/2.

Calculate the Pythagorean triples associated with each pair.
Based on your results, for which values x and y is this identity valid?
a) x = 3, y = 4
b) x = 4, y = 5
c) x = 5, y = 6
d) x = 6, y = 7

Answer 1

The Pythagorean identity is valid for the pair (3, 4) as it forms a classic Pythagorean triple. Options (b), (c), and (d) do not form Pythagorean triples with integer values.

Step-by-step explanation:

To calculate the Pythagorean triples associated with each pair, we use the identity from the Pythagorean theorem: a² + b² = c².

For the pair (5, 4), we solve for c:

• c = √(5² + 4²)
• c = √(25 + 16)
• c = √41
• c = 6.40312 (approx.)

For the pair (1, ½), we solve for c:

• c = √(1² + (½)²)
• c = √(1 + 0.25)
• c = √1.25
• c = 1.118 (approx.)

The Pythagorean identity is valid for triple sets that can form the sides of a right triangle. Examining the options, (a) 3 and 4 form the classic Pythagorean triple (3, 4, 5), making this identity valid. The other options do not produce integers when using the formula and therefore do not form Pythagorean triples.