Question

page 15 of 15 Pythagorean Triples Quick Check 1 of 51 of 5 Items Question Given that (5,12,13) is a Pythagorean triple, identify another example of a Pythagorean triple from the following.(1 point) Responses (50,120,130) left parenthesis 50 comma 120 comma 130 right parenthesis (25,60,39) left parenthesis 25 comma 60 comma 39 right parenthesis (10,12,13) left parenthesis 10 comma 12 comma 13 right parenthesis (15,25,39) left parenthesis 15 comma 25 comma 39 right parenthesis Skip to navigation

Answer 1

To identify another Pythagorean triple, we need to find a set of three integers \( (a, b, c) \) such that \( a^2 + b^2 = c^2 \).

Let's evaluate the options provided:

1. (50, 120, 130): \[ 50^2 + 120^2 = 2500 + 14400 = 16900 \] \[ 130^2 = 16900 \] This set is a Pythagorean triple.

2. (25, 60, 39): \[ 25^2 + 60^2 = 625 + 3600 = 4225 \] \[ 39^2 = 1521 \] This set is not a Pythagorean triple.

3. (10, 12, 13): \[ 10^2 + 12^2 = 100 + 144 = 244 \] \[ 13^2 = 169 \] This set is not a Pythagorean triple.

4. (15, 25, 39): \[ 15^2 + 25^2 = 225 + 625 = 850 \] \[ 39^2 = 1521 \] This set is not a Pythagorean triple.

Based on the evaluations, the only valid Pythagorean triple from the provided options is (50, 120, 130).