Question

Hello! I'm stuck on Pythagorean theorem in geometry. There are some numbers that suppose to have a line on top but I don't know how to put it on top of the number, I just put this `. So, here's the problem: Which side lengths form a right triangle? A. 2,2, v```4``

Answer 1

Choice A: $2,2, \sqrt{4}$

Choice B: 9, 40, 41

Choice C: $\sqrt{5}, 10 and \sqrt{125}$

Answer:

(B)9, 40, 41

Step-by-step explanation:

To check if the sides form a right triangle, you check to see if they satisfy the Pythagorean theorem.

$Hypotenuse^2=Opposite^2+Adjacent^2$

Note that the longest side length is always the hypotenuse.

Choice A: $2,2, \sqrt{4}$

Now, $\sqrt{4}=2$

Therefore:

$2^2\neq 2^2+2^2\\4 \neq 8$

These side lengths form an equilateral triangle. They do not satisfy the theorem.

Choice B: 9, 40, 41

The longest side length is 41.

$41^2=1681$

$40^2+9^2=1681$

Therefore:

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

These side lengths form a right triangle.

Choice C: $\sqrt{5}, 10 and \sqrt{125}$

$\sqrt{5} \approx 2.24 \\ \sqrt{125}\approx11.18$

Therefore, the longest side length is $\sqrt{125}$

$(\sqrt{125})^2=125\\(\sqrt{5})^2+10^2=5+100=105\\\\(\sqrt{125})^2 \neq (\sqrt{5})^2+10^2$

These side lengths do not form a right triangle.