Question

Find the length of the third side of each triangle.

Answer 1

The length of the third side is 1 unit.

Explanation:

Because this is a right triangle, we can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean theorem: a² + b² = c², where variables a and b are the legs of the triangle and c is the hypotenuse

We are going to let a = (12/13) and b = (5/13), though the order does not particularly matter in this case. We are going to plug and play with the theorem, and then simplify as we go.


`((12)/(13))^(2) + ((5)/(13))^(2) = c^(2)\\\\(144)/(169) + (25)/(169) = c^(2)\\\\(144 + 25)/(169) = c^(2)\\ \\ (169)/(169) = c^(2)\\\\1 = c^(2)\\\\√(1) = \sqrt{c^(2)} \\\\c = 1`