To determine which of the given side lengths would form a right triangle with side lengths of 24 and 18, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side), and \( a \) and \( b \) are the other two sides.
Given:
- \( a = 24 \)
- \( b = 18 \)
- \( c \) (hypotenuse) is one of \( 40, 30, 39, \) or \( 51 \)
Let's test each option:
1. For \( c = 40 \):
\[ 24^2 + 18^2 = 576 + 324 = 900 \]
\[ c^2 = 40^2 = 1600 \]
\( 900 \neq 1600 \)
2. For \( c = 30 \):
\[ 24^2 + 18^2 = 576 + 324 = 900 \]
\[ c^2 = 30^2 = 900 \]
\( 900 = 900 \)
This matches the Pythagorean theorem.
3. For \( c = 39 \):
\[ 24^2 + 18^2 = 576 + 324 = 900 \]
\[ c^2 = 39^2 = 1521 \]
\( 900 \neq 1521 \)
4. For \( c = 51 \):
\[ 24^2 + 18^2 = 576 + 324 = 900 \]
\[ c^2 = 51^2 = 2601 \]
\( 900 \neq 2601 \)
Therefore, the side lengths of 24, 18, and 30 would form a right triangle.
Side lengths of 24, 18 and ______ would form a right triangle.
40
30
39
51
1 answer
1 answer