Find all values of t such that t - 1, t + 1, and 8 + t could be the lengths of the sides of a right triangle.
+2668 If \(8 + t\) is the hypotenuse, we have the equation \((8 + t)^2 = (t + 1)^2 + (t - 1)^2\)
Solve for t, and use the positive, real values
If \(t + 1\) is the hypotenuse, we have the equation \((1 + t)^2 = (t + 8)^2 + (t - 1)^2\)
Again, solve for t, and use positive, real values.
If \(t - 1\) is the hypotenuse, we have the equation \((t - 1)^2 = (t + 8)^2 + (t + 1)^2\)
Solve for t, and use the real, positive values.
Can you take it from here?
