A right triangle has side lengths 12 centimeters and 14 centimeters. Name two possible side lengths for the third side, and explain how you solved for each.

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18.4 or 7.2

Step-by-step explanation:

The third side can be hypotenuse or base/perpendicular

If third side is hypotenuse

H²=B²+P²

H² = 12²+14²

H=18.4cm

If third side is base/perpendicular

14²=12² + P²

P = 7.2

If 12 and 14 are both side lengths then we solve for the hypotenuse:

hypotenuse^2 = 12^2 + 14^2

hypotenuse^2 = 144 + 196

hypotenuse^2 = 340

hypotenuse = sq root (340) = 18.4390889146

If hypotenuse = 14, then third side equals:

(3rd side) ^2 = 14^2 - 12^2

(3rd side) ^2 = 196 - 144

(3rd side) ^2 = 52

3rd side = sq root (52) = 7.2111025509