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:

To determine which set of numbers can represent the side lengths of a right triangle, we use the Pythagorean theorem, which states that for a right triangle with side lengths \(a\), \(b\) (the legs), and \(c\) (the hypotenuse, the longest side), \(a^2 + b^2 = c^2\). We will check each option:

Step 1: Check 8, 12, 15

The longest side is 15. Calculate \(8^2 + 12^2\) and \(15^2\):
\(8^2 = 64\), \(12^2 = 144\), so \(8^2 + 12^2 = 64 + 144 = 208\)
\(15^2 = 225\)
Since \(208
eq 225\), this is not a right triangle.

Step 2: Check 10, 24, 26

The longest side is 26. Calculate \(10^2 + 24^2\) and \(26^2\):
\(10^2 = 100\), \(24^2 = 576\), so \(10^2 + 24^2 = 100 + 576 = 676\)
\(26^2 = 676\)
Since \(676 = 676\), this satisfies the Pythagorean theorem. But we will check the other options to be thorough.

Step 3: Check 12, 20, 25

The longest side is 25. Calculate \(12^2 + 20^2\) and \(25^2\):
\(12^2 = 144\), \(20^2 = 400\), so \(12^2 + 20^2 = 144 + 400 = 544\)
\(25^2 = 625\)
Since \(544
eq 625\), this is not a right triangle.

Step 4: Check 15, 18, 20

The longest side is 20. Calculate \(15^2 + 18^2\) and \(20^2\):
\(15^2 = 225\), \(18^2 = 324\), so \(15^2 + 18^2 = 225 + 324 = 549\)
\(20^2 = 400\)
Since \(549
eq 400\), this is not a right triangle.

Answer:

B. 10, 24, 26