Question

Which side lengths form a right triangle? Choose all answers that apply: 4, V8,24 5,5,5 4, 7.5, 8.5 Stuck? Watch a video or use a hint.

Answer 1

According to the Pythagorean Theorem, for a Right triangle:

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

Where "a" is the hypotenuse and "b" and "c" are the legs of the Right triangle.

Let's check the side lengths given in each option:

A) The hypotenuse would be:

`a=24`

So, if you apply the Pythagorean Theorem, you get:

`\begin{gathered} 24^2=4^2+(\sqrt[]{8})^2 \\ 576\\e34 \end{gathered}`

These side lenghts do not form a Right triangle.

B) Since all the sides of this triangle have equal length, it is not a Right triangle, but an Equilateral triangle.

C) The hypotenuse of this triangle would be:

`a=8.5`

Then, applying the Pythagorean Theorem, you get:

`\begin{gathered} (8.5)^2=(4)^2+(7.5)^2 \\ 72.25=72.25 \end{gathered}`

These side lenghts form a Right triangle.

The answer is: Option C