Question

Which measures are the sides lengths of a right triangle?a)4cm 12cm 8cmb)5cm 12cm 10cmc)16cm 4cm 6cmd)30cm 12cm 6cm

Answer 1

For the length of a side of a triangle to be trigonometry triple.

Square of the hypotenuse(Longest side) = square of opposite + square of adjacent

$\begin{gathered} \text{opposite}^2+adjacent^2=hypotenuse^2 \\ 4\operatorname{cm}\text{ , 12cm , 8cm} \\ 4^2+8^2\text{ }\ne12^2\text{ 80 }\ne\text{ 144} \\ 5\operatorname{cm}\text{ , 12cm , 10cm} \\ 5^2+10^2\text{ }\ne12^2 \\ 125\text{ }\ne\text{ 144} \\ 16\operatorname{cm}\text{ , 4cm , 6cm} \\ 4^2+6^2\text{ }\ne16^2 \\ 52\text{ }\ne\text{ 256} \\ 30\operatorname{cm}\text{ , 12cm , 6cm } \\ 6^2+12^2\text{ }\ne30^2 \\ 180\text{ }\ne\text{ 900} \end{gathered}$

Hence, none of the options are the lengths of the sides of a right triangle.