Question Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point) Responses No, because 369 is not equal to 100. No, because 369 is not equal to 100. No, because 244 is not equal to 225. No, because 244 is not equal to 225. No, because 22 is not equal to 15. No, because 22 is not equal to 15. No, because 325 is not equal to 144.
No, because 325 is not equal to 144.
Question If the equation 18^2 + b^2 = 30^2 is found to be true, what do we know about the triangle?(1 point) Responses The triangle is a right triangle with a missing side of 34.99. The triangle is a right triangle with a missing side of 34.99. The triangle is a right triangle, and the hypotenuse is 18. The triangle is a right triangle, and the hypotenuse is 18. The triangle is a right triangle, and the legs are 30 and 24. The triangle is a right triangle, and the legs are 30 and 24. The triangle is a right triangle with a missing leg length of 24. The triangle is a right triangle with a missing leg length of 24.
The triangle is a right triangle with a missing leg length of 24.
To determine if the triangle with sides 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem. The converse states that if the square of the longest 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 longest side is 15. So, we need to check if 15^2 is equal to the sum of the squares of 10 and 12.
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
To determine whether 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 sum of the squares of the shorter sides (a^2 + b^2) is equal to the square of the longest side (c^2).
In this case, the given sides are 15, 10, and 12. We can calculate the sum of the squares of the shorter sides as follows:
(10^2) + (12^2) = 100 + 144 = 244
The square of the longest side can be calculated as:
(15^2) = 225
Comparing these values, we see that 244 is not equal to 225. Therefore, the equation (a^2 + b^2 = c^2) is not satisfied, and we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
Hence, the correct response is: No, because 244 is not equal to 225.