Question

Select three measures that could be the threeside lengths of a right triangle.17 cm20 cm21 cm29 cm

Answer 1

To know if the three side length of a triangle makes a right angle or not, the three sides must be a Pythagoras triple.

This means the sum of the squares of the two shortest sides (a and b) must be equal to the square of the longest side (c).

`a^2+b^2=c^2`

When we find the squares of all the sides,

`\begin{gathered} 17^2=289 \\ 20^2=400 \\ 21^2=441 \\ 29^2=841 \end{gathered}`

From the squares above, the one that will give a right triangle from Pythagoras theorem will be,

`\begin{gathered} 20^2+21^2=29^2 \\ 400+441=841 \\ 841=841 \\ \\ S\text{ ince,} \\ a^2+b^2=c^2,\text{ then 20,21 and 29 are Pythagoras triples } \\ \text{They will be the thr}e\text{ sides of a right triangle} \\ S\text{ ince they obey the Pythagoras theorem.} \end{gathered}`

Therefore, 20cm, 21cm and 29cm are the side lengths of a right triangle.

From the squares above, the one that will give a right triangle from Pythagoras theorem will be,

`\begin{gathered} 20^2+21^2=29^2 \\ 400+441=841 \\ 841=841 \\ \\ S\text{ ince,} \\ a^2+b^2=c^2,\text{ then 20,21 and 29 are Pythagoras triples } \\ \text{They will be the thr}e\text{ sides of a right triangle} \\ S\text{ ince they obey the Pythagoras theorem.} \end{gathered}`

Therefore, 20cm, 21cm and 29cm are the side lengths of a right triangle.