Pythagorean Theorem Proofs Quick Check 3 of 53 of 5 Items 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 325 is not equal to 144. No, because 325 is not equal to 144. No, because 22 is not equal to 15. No, because 22 is not equal to 15. No, because 244 is not equal to 225. No, because 244 is not equal to 225. No, because 369 is not equal to 100
The correct response is: No, because 325 is not equal to 144.
f the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point) Responses 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 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 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 legs are 30 and 24.
The correct response is: The triangle is a right triangle with a missing leg length of 24.
If the equation%C2%A0182%C2%A0+%C2%A0b2%C2%A0=%C2%A0302 is found to be true, what do we know about the triangle?(1 point) Responses 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 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%C2%A0and 24.
The correct response is: The triangle is a right triangle, and the legs are 30 and 24.
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 square of the longest side is equal to the sum of the squares of the other two sides.
First, let's identify the longest side. In this case, the longest side is 15.
Next, we calculate the sum of the squares of the other two sides:
10^2 + 12^2 = 100 + 144 = 244
Finally, we compare the sum of the squares to the square of the longest side:
15^2 = 225
Since 244 is not equal to 225, which means the sum of the squares of the shorter sides is not equal to the square of the longest side, we can conclude that the triangle is not a right triangle.
Therefore, the correct answer is "No, because 244 is not equal to 225."