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: Apply Pythagorean theorem

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

For \(8,12,15\):

\(8^{2}+12^{2}=64 + 144=208\), \(15^{2}=225\). Since \(208
eq225\).

For \(10,24,26\):

\(10^{2}+24^{2}=100+576 = 676\), \(26^{2}=676\). Since \(10^{2}+24^{2}=26^{2}\).

For \(12,20,25\):

\(12^{2}+20^{2}=144 + 400=544\), \(25^{2}=625\). Since \(544
eq625\).

For \(15,18,20\):

\(15^{2}+18^{2}=225+324 = 549\), \(20^{2}=400\). Since \(549
eq400\).

Answer:

\(10,24,26\)