Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)
The Converse of the Pythagorean Theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
In this case, the longest side is 15. According to the Pythagorean Theorem, if the triangle is a right triangle, 15² should be equal to 10² + 12².
15² = 225
10² + 12² = 100 + 144 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle, as it does not satisfy the Converse of the Pythagorean Theorem.
The converse of the Pythagorean Theorem states that if the square of the length 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.
To determine if the triangle is a right triangle, we can square the lengths of the other two sides and check if they add up to the square of the longest side.
The squares of the lengths of the other two sides are:
10^2 = 100
12^2 = 144
Adding these two values together gives us 100 + 144 = 244.
The square of the longest side, 15^2, is 225.
Since 244 is not equal to 225, 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, we can use the Converse of the Pythagorean Theorem. The Converse of the Pythagorean Theorem 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, we can identify the longest side by comparing the given side lengths. The side with length 15 is the longest side. Now, we need to square the length of the longest side (15 in this case), and also square the lengths of the other two sides (10 and 12).
15^2 = 225
10^2 = 100
12^2 = 144
Next, we need to check if the sum of the squares of the other two sides is equal to the square of the longest side:
100 + 144 = 244
Since 244 is not equal to 225, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle, according to the Converse of the Pythagorean Theorem.