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

(Choice A)
A
3
,
27
,
6
3,
27

,63, comma, square root of, 27, end square root, comma, 6

(Choice B)
B
8
,
15
,
17
8,15,178, comma, 15, comma, 17

(Choice C)
C

4, 7.5, 8.54,7.5,8.5

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

a^2 + b^2 = c^2a  

2

+b  

2

=c  

2

a, squared, plus, b, squared, equals, c, squared

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

[How can I tell which side is the hypotenuse?]

Hint #22 / 5

Let's check each set of numbers:

\begin{aligned} a^2 + b^2 &= c^2 4^2 +\sqrt8^2 &\stackrel{\large?}{=} 24^2 16 + 8&\stackrel{\large?}{=} 576 24&\neq 576 \end{aligned}  

a  

2

+b  

2

4  

2

+  

8

2

16+8

24

=c  

2

=

?

24  

2

=

?

576



=576

The side lengths 4, \sqrt8, 244,  

8

,244, comma, square root of, 8, end square root, comma, 24 do not form a right triangle.

Hint #33 / 5

\begin{aligned} a^2 + b^2 &= c^2 5^2 + 5^2 &\stackrel{\large?}{=} 5^2 25+ 25&\stackrel{\large?}{=} 25 50&\neq 25 \end{aligned}  

a  

2

+b  

2

5  

2

+5  

2

25+25

50

=c  

2

=

?

5  

2

=

?

25



=25

The side lengths 5, 5, 55,5,55, comma, 5, comma, 5 do not form a right triangle.

Hint #44 / 5

\begin{aligned} a^2 + b^2 &= c^2 4^2 + 7.5^2 &\stackrel{\large?}{=} 8.5^2 16+ 56.25&\stackrel{\large?}{=} 72.25 72.25&\stackrel{\checkmark}{=} 72.25 \end{aligned}  

a  

2

+b  

2

4  

2

+7.5  

2

16+56.25

72.25

=c  

2

=

?

8.5  

2

=

?

72.25

=

✓

72.25