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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.

 Jul 16, 2022
 #1
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Use triangle inequality! :D What kind of inequalities can you form?

 Jul 16, 2022
 #2
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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?

 Jul 16, 2022

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