Question

which set of numbers can represent the side lengths, in centimeters, of a right triangle?
○ 8, 12, 15
○ 10, 24, 26
○ 12, 20, 25
○ 15, 18, 20

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check 8, 12, 15

Calculate \(8^2 + 12^2 = 64 + 144 = 208\), \(15^2 = 225\). \(208
eq225\), so not a right triangle.

Step3: Check 10, 24, 26

Calculate \(10^2 + 24^2 = 100 + 576 = 676\), \(26^2 = 676\). \(676 = 676\), so this satisfies the theorem.

Step4: Check 12, 20, 25 (optional, since we found a match)

Calculate \(12^2 + 20^2 = 144 + 400 = 544\), \(25^2 = 625\). \(544
eq625\), not a right triangle.

Step5: Check 15, 18, 20 (optional)

Calculate \(15^2 + 18^2 = 225 + 324 = 549\), \(20^2 = 400\). \(549
eq400\), not a right triangle.

Answer:

B. 10, 24, 26