Question
use the converse of the Pythagorean theorem explain whether a triangle with sides 15, 10, and 12 is a right triangle
Answers
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GPT 3.5
The converse of the Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
In this case, the sides of the triangle are 15, 10, and 12. The longest side is 15, so according to the Pythagorean theorem, if the square of 15 is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.
In this case, the sides of the triangle are 15, 10, and 12. The longest side is 15, so according to the Pythagorean theorem, if the square of 15 is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.