Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10 and
12 is a right triangle (1 point)
O No, because 244 is not equal to 225
No, because 22 is not equal to 15.
No, because 325 is not equal to 144.
No, because 369 is not equal to 100.
The correct answer is:
No, because 325 is not equal to 144.
If a triangle satisfies the condition a^2 + b^2 = c^2 (where a, b, and c are the lengths of the sides of the triangle), then it is a right triangle. In this case, the lengths of the sides are given as 15, 10, and 12.
If we substitute these values into the equation, we get:
15^2 + 10^2 = 12^2
225 + 100 = 144
325 ≠ 144
Since the equation is not satisfied, the triangle is not a right triangle.
To determine if a triangle is a right triangle, we can use the converse of the Pythagorean theorem. The converse of the Pythagorean theorem states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle.
In this case, let's check if the triangle with sides 15, 10, and 12 is a right triangle using the converse of the Pythagorean theorem.
First, we calculate the square of the sides:
15^2 = 225
10^2 = 100
12^2 = 144
Next, we check if the sum of the squares of the two shorter sides equals the square of the longest side:
225 + 100 = 325
Since 325 is not equal to 144, the triangle with sides 15, 10, and 12 is not a right triangle.
To determine whether a triangle is a right triangle, we can use the Converse of the Pythagorean Theorem. The theorem states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side (hypotenuse), then the triangle is a right triangle.
In this case, the given side lengths of the triangle are 15, 10, and 12. Let's calculate the squares of these side lengths:
15^2 = 225
10^2 = 100
12^2 = 144
Next, we need to check if the sum of the squares of the two shorter sides is equal to the square of the longest side. So, we have:
225 + 100 = 325
Comparing this sum with the square of the longest side:
325 ≠ 144
Since the sum of the squares of the two shorter sides (325) is not equal to the square of the longest side (144) in this case, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.