Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 10, 10 and 12 is a right triange
No, because 244 is not equal to 225
No because 359 is not equal to 100.
No because 22 is not equal to 15.
O to because 325 is not equal to 144
No, because the converse of the Pythagorean theorem states that if the square of the longest side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. In this case, 12^2 is not equal to 10^2 + 10^2, so the triangle is not a right triangle.
To determine whether a triangle with sides 10, 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 (the hypotenuse) is equal to the sum of the squares of the other two sides.
In this case, the longest side is 12. Now we need to calculate the sum of the squares of the other two sides:
First side: 10^2 = 100.
Second side: 10^2 = 100.
Now, let's check if the square of the longest side is equal to the sum of the squares of the other two sides:
12^2 = 144.
The sum of the squares of the other two sides is 100 + 100 = 200.
Since 144 is not equal to 200, according to the Converse of the Pythagorean Theorem, the triangle with sides 10, 10, and 12 is not a right triangle.
To determine whether a triangle with sides 10, 10, and 12 is a right triangle, we can apply the Converse of the Pythagorean Theorem. The Converse of the Pythagorean Theorem states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.
In this case, we need to check if the sum of the squares of the two shorter sides (10 and 10) is equal to the square of the longest side (12).
To do this, we can calculate the square of each side:
- The square of the first side (10) is 10^2 = 100.
- The square of the second side (10) is also 10^2 = 100.
- The square of the third side (12) is 12^2 = 144.
Next, we add the squares of the two shorter sides:
100 + 100 = 200.
Finally, we compare this sum with the square of the longest side:
200 is not equal to 144.
Since the sum of the squares of the two shorter sides (200) is not equal to the square of the longest side (144), we can conclude that the triangle with sides 10, 10, and 12 is not a right triangle.