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

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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 though you could easily do

vbbv

step-by-step explanation:

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option