Question

Determine which of the following to be the side measurement of a right triangle and place them in the correct category.

Answer 1

Given: The following side measurement of different triangles

`\begin{gathered} A=10,24,26 \\ B=5,12,13 \\ C=3,4,6| \\ D=12,16,30 \end{gathered}`

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

`\begin{gathered} A=10,24,26 \\ 10^2+24^2=26^2 \\ 100+576=676 \\ 676=676 \end{gathered}`
`\begin{gathered} B=5,12,13 \\ 5^2+12^2=13^2 \\ 25+144+169 \\ 169=169 \end{gathered}`
`\begin{gathered} C=3,4,6 \\ 3^2+4^2=6^2 \\ 9+16=36 \\ 25\\e36 \end{gathered}`
`\begin{gathered} D=12,16,30 \\ 12^2+16^2=30^2 \\ 144+256=900 \\ 400\\e900 \end{gathered}`

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