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, √(4)`

Choice B: 9, 40, 41

Choice C:
`√(5), 10$ and √(125)`

Answer:

(B)9, 40, 41

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, √(4)`

Now,
`√(4)=2`

Therefore:

`2^2\\eq 2^2+2^2\\4 \\eq 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:
`√(5), 10$ and √(125)`

`√(5) \approx 2.24 \\ √(125)\approx11.18`

Therefore, the longest side length is
`√(125)`

`(√(125))^2=125\\(√(5))^2+10^2=5+100=105\\\\(√(125))^2 \\eq (√(5))^2+10^2`

These side lengths do not form a right triangle.