Which side lengths form a right triangle? Choose all answers that apply: (Answers in picture)
Accepted Solution
A:
Answer:4, 7.5, 8.54,7.5,8.5Step-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