Final answer:
To determine if a triangle is a right triangle, we can apply the Pythagorean theorem to check if the sum of the squares of the two shorter sides is equal to the square of the longest side. Based on this, we can determine that (b) 8, 15, 17 and (c) 7, 10, 12 are right triangles, while (a) 10, 24, 26 and (d) 13, 20, 26 are not.
Step-by-step explanation:
To determine whether a triangle with given side lengths is a right triangle, we can apply the Pythagorean theorem. The theorem states that for a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse). So, by calculating the squares of the given side lengths:
(a) 10² + 24² = 100 + 576 = 676
(b) 8² + 15² = 64 + 225 = 289
(c) 7² + 10² = 49 + 100 = 149
(d) 13² + 20² = 169 + 400 = 569
We can see that:
(a) 10, 24, 26 - Not a right triangle
(b) 8, 15, 17 - Right triangle
(c) 7, 10, 12 - Right triangle
(d) 13, 20, 26 - Not a right triangle