Given: The following side measurement of different triangles
[tex]\begin{gathered} A=10,24,26 \\ B=5,12,13 \\ C=3,4,6| \\ D=12,16,30 \end{gathered}[/tex]
To Determine: Which of the measurement is for a right triangle and the one that is not
Solution
Step 1: Define Pythagoras triples
We would determine if the measurement given obeys pythagoras triples. Pythagoras triples are 3 measurement of a right triangle which follows the pythagoras theorem. Pythagoras theorem states that the square of the hypothenuse is equal to the sum of the squares of the two other sides. Note that the hypothenuse is the longest side
Step 2: Verify each of the given measurements
[tex]\begin{gathered} A=10,24,26 \\ 10^2+24^2=26^2 \\ 100+576=676 \\ 676=676 \end{gathered}[/tex][tex]\begin{gathered} B=5,12,13 \\ 5^2+12^2=13^2 \\ 25+144+169 \\ 169=169 \end{gathered}[/tex][tex]\begin{gathered} C=3,4,6 \\ 3^2+4^2=6^2 \\ 9+16=36 \\ 25\ne36 \end{gathered}[/tex][tex]\begin{gathered} D=12,16,30 \\ 12^2+16^2=30^2 \\ 144+256=900 \\ 400\ne900 \end{gathered}[/tex]
It can be seen from the above calculations that A and B are pythagoras triples, while C and D did not obey pythagoras triples
Hence
10,24,26 and 5, 12, 13 are side measurements of right triangles
While 3,4,6 and 12, 16, 30 are not right triangles
