If a triangle has sides of lengths 5,8 and 12 it is a right triangle ??!! True or false? Can someone please answer
for a right triangle, you'd need
5^2 + 8^2 = 12^2
Is this true?
Clearly not, since odd+even = odd, which you do not have.
To determine if the triangle is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's check if this holds true for the given triangle:
- Side length 5: 5^2 = 25
- Side length 8: 8^2 = 64
- Side length 12: 12^2 = 144
Now, we need to add the squares of the two smaller side lengths:
25 + 64 = 89
Since 89 is not equal to 144, the given triangle is not a right triangle. Therefore, the statement is false.
To determine if a triangle is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's apply this theorem to the given triangle with side lengths 5, 8, and 12:
• The longest side in this case is 12, which we'll assume is the hypotenuse.
• The other two sides are 5 and 8.
Using the theorem, we need to check if 12^2 is equal to 5^2 + 8^2:
12^2 = 144
5^2 + 8^2 = 25 + 64 = 89
Since 144 is not equal to 89, this triangle does not satisfy the Pythagorean theorem. Therefore, it is not a right triangle.
So, the statement "If a triangle has sides of lengths 5, 8, and 12, it is a right triangle" is false.