Question
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15,10 , and 12 is a right triangle
No, because 325 is not equal to 144 .
No, because 22 is not equal to 15 .
No, because 369 is not equal to 100 .
No, because 244 is not equal to 225 .
No, because 325 is not equal to 144 .
No, because 22 is not equal to 15 .
No, because 369 is not equal to 100 .
No, because 244 is not equal to 225 .
Ask by Fleming Riley. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The triangle with sides 15, 10, and 12 is not a right triangle because
Solution
To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we need to check if the square of the longest side is equal to the sum of the squares of the other two sides.
Given sides: 15, 10, and 12
The longest side is 15.
According to the Converse of the Pythagorean Theorem:
where
Substitute the given values:
Since 244 is not equal to 225, the triangle with sides 15, 10, and 12 is not a right triangle.
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Simplify this solution Beyond the Answer
To determine if the triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we need to check if the square of the longest side (15) is equal to the sum of the squares of the other two sides (10 and 12). Calculating those, we have 15² = 225 and 10² + 12² = 100 + 144 = 244. Since 225 is not equal to 244, the triangle is not a right triangle.
If you want to remember this for future questions, it’s helpful to always identify the longest side first! The Converse of the Pythagorean Theorem basically states that if the square of the longest side is not equal to the sum of the squares of the other two sides, the triangle is not right-angled. So, keep that handy for next time!
