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Which side lengths form a right triangle? Choose all answers that apply:​

Which side lengths form a right triangle? Choose all answers that apply:​-example-1

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Answer:

Option C, 30 40 50

Explanation:

In order for 3 sides to form a right triangle, there are two options:

1.) Both sides are equal, and the hypotenuse is sqrt(2) * the length of the sides.

2.) One side is (sqrt(3)) / 2 * h and the other side is 1/2 * h and the hypotenuse is just h.

Step 1: Determine if A is correct

No, Option 1 is automatically thrown away because no sides are equal.

No, Option 2 isn't possible because if you put the sides in any arrangement it won't work.

Step 2: Determine if B is correct

No, Option 1 is once again thrown away because no sides are equal.

No, Option 2 is not possible once again because in whatever arrangement you put the sides in, it won't work.

Step 2: Determine if C is correct

No, Option 1 is once again thrown out because no sides are in equal length.

No, Option 2 is neither possible since you can't organize it in a way to fit the pattern.

However, there is an exception called the 3-4-5 triangle which forms a right triangle. In this example, we have a 30-40-50 triangle that forms into a right triangle.

Answer: Option C, 30 40 50

Which side lengths form a right triangle? Choose all answers that apply:​-example-1
Which side lengths form a right triangle? Choose all answers that apply:​-example-2
Which side lengths form a right triangle? Choose all answers that apply:​-example-3
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