Question

Which side lengths form a right triangle?

Choose all answers that apply:

(Choice A)
2,2, square root of 4

(Choice B)
9, 40, 41

(Choice C)
square root of 5, 10, square root of 125

Answer 1

C (9, 40, 41)

Step-by-step explanation:We can use the Pythagorean Theorem to see if the side lengths will form a right triangle.The equation for the Pythagorean Theorem is a2+b2=c2a2+b2=c2

where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.

Let's check each set of numbers:a2+b2=c222+224+48≠4a2+b222+224+48​=c2=?4​2=?4​=4​

The side lengths 2,2,42,2,4​2, comma, 2, comma, square root of, 4, end square root do not form a right triangle.Hint #33 / 5a2+b2=c292+40281+16001681a2+b292+40281+16001681​=c2=?412=?1681=✓1681​

The side lengths 9,40,419,40,419, comma, 40, comma, 41 do form a right triangle.Hint #44 / 5a2+b2=c252+1025+100105≠125a2+b25​2+1025+100105​=c2=?125​2=?125​=125​

The side lengths 5,10,1255​,10,125​square root of, 5, end square root, comma, 10, comma, square root of, 125, end square root do not form a right triangle.Hint #55 / 5The side lengths that form a right triangle are: 9,40,419,40,41

Answer 2

B, C

Explanation:

A: √4 = 2, so the side lengths form an equilateral triangle, not a right triangle.

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B: √(9²+40²) = 41 . . . . these form a right triangle

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C: √(5² +10²) = √125 . . . . these form a right triangle