Find all values of $t$ such that $t - 1$, $t + 1$, and $4$ could be the lengths of the sides of a right triangle.

Question

Foster

Mathematics

31 July, 10:50

Find all values of $t$ such that $t - 1$, $t + 1$, and $4$ could be the lengths of the sides of a right triangle.

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Trevin Austin · Answer 1

side 1: t - 1

side 2: t + 1

side 3: 4

side 1 + side 2 > side 3 & side 2 + side 3 > side 1 & side 3 + side 1 > side 2

(t - 1) + (t + 1) > 4 (t + 1) + (4) > (t - 1) (4) + (t - 1) > (t + 1)

2t > 4 t + 5 > t - 1 t + 3 > t + 1

t > 2 5 > - 1 (TRUE) 3 > 1 (TRUE)

Answer: t > 2