question 2\nsuppose triangles p, q, and r have sides with the given measurements.\n- triangle p: 12, 24, and…

question 2\nsuppose triangles p, q, and r have sides with the given measurements.\n- triangle p: 12, 24, and 30\n- triangle q: 9, 40, and 41\n- triangle r: 5, 18, and 21\nwhich triangle is a right triangle? explain your reasoning.

question 2\nsuppose triangles p, q, and r have sides with the given measurements.\n- triangle p: 12, 24, and 30\n- triangle q: 9, 40, and 41\n- triangle r: 5, 18, and 21\nwhich triangle is a right triangle? explain your reasoning.

Answer

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, (a^2 + b^2 = c^2) (where (c) is the longest side).

Step2: Check Triangle P (12, 24, 30)

Calculate (12^2 + 24^2) and (30^2).
(12^2 = 144), (24^2 = 576), so (144 + 576 = 720).
(30^2 = 900).
Since (720 \neq 900), not a right triangle.

Step3: Check Triangle Q (9, 40, 41)

Calculate (9^2 + 40^2) and (41^2).
(9^2 = 81), (40^2 = 1600), so (81 + 1600 = 1681).
(41^2 = 1681).
Since (81 + 1600 = 1681), satisfies (a^2 + b^2 = c^2).

Step4: Check Triangle R (5, 18, 21)

Calculate (5^2 + 18^2) and (21^2).
(5^2 = 25), (18^2 = 324), so (25 + 324 = 349).
(21^2 = 441).
Since (349 \neq 441), not a right triangle.

Answer:

Triangle Q (9, 40, 41) is a right triangle because (9^2 + 40^2 = 41^2) (81 + 1600 = 1681), satisfying the Pythagorean theorem.