Question

which side is hypotenuse? triangle with vertices t, s, r; right angle at s; sides: ts=4, sr=3, tr=5; options (partial): 3, 4, 5, all of the above

Explanation:

Step1: Recall hypotenuse definition

In a right - triangle, the hypotenuse is the side opposite the right angle and is the longest side.

Step2: Identify the right angle and sides

The right angle is at \(S\). The sides of the triangle are of lengths \(3\) ( \(RS\) ), \(4\) ( \(TS\) ) and \(5\) ( \(TR\) ). Since \(5\) is the longest side and it is opposite the right angle at \(S\), the hypotenuse is the side with length \(5\) (i.e., \(TR\)).

Answer:

The side with length \(5\) (the side labeled as \(5\) connecting \(T\) and \(R\)) is the hypotenuse. So the correct option is the one with \(5\) (e.g., if the options are as per the colors, the green option with \(5\)).