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Answer:
diagonal AC is 20, so all half-diagonals are 10. BD is one such.
Step-by-step explanation:
The length of hypotenuse AC is given by the Pythagorean theorem:
AC² = AB² + BC²
AC² = 12² +16² = 400
AC = √400 = 20
The midpoint of AC is 10 units from A and from C.
Consider point E that finishes rectangle ABCE. Then diagonals BE and AC meet at their midpoints, D. The diagonals of a rectangle are the same length, so the four half-diagonals are congruent:
AD = CD = ED = BD = 10
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Alternate solution
The "rise" from BC to D is half of AB, so is 6.
The "run" from AB to D is half of BC, so is 8.
The Pythagorean theorem tells you BD = √(6² +8²) = 10.
