Question
Does a traingle with side lengths of 6, 10, and 8 form a right triangle?
Answers
GPT-4o mini
To determine whether a triangle with side lengths of 6, 10, and 8 can form a right triangle, we can use the Pythagorean theorem. The theorem states that for a right triangle with sides \(a\), \(b\), and hypotenuse \(c\) (where \(c\) is the longest side):
\[
c^2 = a^2 + b^2
\]
In this case, the longest side is 10, so we can set \(c = 10\), \(a = 6\), and \(b = 8\). Now we can check if the equation holds:
\[
10^2 = 6^2 + 8^2
\]
Calculating each side:
\[
100 = 36 + 64
\]
\[
100 = 100
\]
Since both sides of the equation are equal, the triangle with side lengths of 6, 10, and 8 does indeed form a right triangle.
\[
c^2 = a^2 + b^2
\]
In this case, the longest side is 10, so we can set \(c = 10\), \(a = 6\), and \(b = 8\). Now we can check if the equation holds:
\[
10^2 = 6^2 + 8^2
\]
Calculating each side:
\[
100 = 36 + 64
\]
\[
100 = 100
\]
Since both sides of the equation are equal, the triangle with side lengths of 6, 10, and 8 does indeed form a right triangle.