Question

Which set of side lengths can be used to form a right

triangle?
2, 3, 4
10, 20, 30
30, 40, 50
4, 5, 6

Answer 1

Answer: C) 30, 40, 50

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Step-by-step explanation:

Use the pythagorean theorem to determine if we have a right triangle or not.

Choice A is not a right triangle because

a^2+b^2 = c^2

2^2+3^2 = 4^2

4+9 = 16

13 = 16

is false. So a triangle with sides a = 2, b = 3, c = 4 is not a right triangle

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The same applies to choice B as well

a = 10, b = 20, c = 30

a^2+b^2 = c^2

10^2 + 20^2 = 30^2

100+400 = 900

500 = 900 is false

Cross choice B off the list.

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Choice C is true however

a = 30, b = 40, c = 50

a^2 + b^2 = c^2

30^2 + 40^2 = 50^2

900 + 1600 = 2500

2500 = 2500 is true

So a triangle with sides 30, 40, 50 is a right triangle.

It is based off the 3,4,5 right triangle (multiply all three sides by 10 to scale it up).

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For the sake of completeness, let's check choice D.

a = 4, b = 5, c = 6

a^2 + b^2 = c^2

4^2 + 5^2 = 6^2

16 + 25 = 36

41 = 36 is false

So a triangle with sides 4,5,6 is not a right triangle.

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Note: for each answer choice, the longest side is always c. The order of the other two sides does not matter. The convention is usually
`a \le b < c` though you could easily do
`b \le a < c`