Question
Which math sentence can be used to determine if this triangle is a right triangle?
A triangle has side lengths 12, 15, 18.
12 + 15 = 18
12 squared + 15 squared = 18 squared
12 + 18 = 15
12 squared + 18 squared = 15 squared
A triangle has side lengths 12, 15, 18.
12 + 15 = 18
12 squared + 15 squared = 18 squared
12 + 18 = 15
12 squared + 18 squared = 15 squared
Answers
GPT-4o mini
To determine if a triangle with side lengths 12, 15, and 18 is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we first identify the longest side, which is 18. Therefore, we set up the equation:
\[ 12^2 + 15^2 = 18^2 \]
Now, we can calculate the squares:
- \( 12^2 = 144 \)
- \( 15^2 = 225 \)
- \( 18^2 = 324 \)
Then we sum \( 12^2 \) and \( 15^2 \):
\[ 144 + 225 = 369 \]
Since 369 does not equal \( 324 \), we conclude that:
\[ 12^2 + 15^2 \neq 18^2 \]
Thus, the math sentence you should use is:
**\( 12^2 + 15^2 = 18^2 \)**
This indicates whether or not the triangle is a right triangle. In this case, since the equation does not hold true, the triangle with sides 12, 15, and 18 is not a right triangle.
In this case, we first identify the longest side, which is 18. Therefore, we set up the equation:
\[ 12^2 + 15^2 = 18^2 \]
Now, we can calculate the squares:
- \( 12^2 = 144 \)
- \( 15^2 = 225 \)
- \( 18^2 = 324 \)
Then we sum \( 12^2 \) and \( 15^2 \):
\[ 144 + 225 = 369 \]
Since 369 does not equal \( 324 \), we conclude that:
\[ 12^2 + 15^2 \neq 18^2 \]
Thus, the math sentence you should use is:
**\( 12^2 + 15^2 = 18^2 \)**
This indicates whether or not the triangle is a right triangle. In this case, since the equation does not hold true, the triangle with sides 12, 15, and 18 is not a right triangle.