Question

I need help with this geometry question I’m confused for some reason.

Answer 1

We are asked to determine which of the triangles is a right triangle. To do that we can apply the Pythagorean theorem, taking the larger side as the hypotenuse. If the Equality of the Pythagorean theorem holds, then the triangle is a right triangle.

Let's take triangle P. The largest side is 30, therefore, we take this as the hypotenuse. The Pythagorean theorem is as follows:

$h^2=a^2+b^2$

Where:

$\begin{gathered} h=\text{ hypotenuse} \\ a,b=\text{ sides} \end{gathered}$

Now we substitute the values:

$30^2=12^2+24^2$

Now we solve the squares:

$900=144+576$

Adding the terms:

$900=720$

Since the terms on the right side and the left side are not equal, this means that the given triangle is not a right triangle.

Now, let's do the same procedure for triangle Q. We have that the hypotenuse in this triangle is 41. Therefore, substituting in the Pythagorean theorem we get:

$41^2=40^2+9^2$

Solving the square:

$1681=1600+81$

Adding the terms:

$1681=1681$

Since we got the same result on both sides this means that the triangle Q is a right triangle.