Answer:
C. 2 units
Step-by-step explanation:
The ratio of side lengths in an isosceles right triangle is ...
1 : 1 : √2
If you don't already have this memorized, you can figure it out using the Pythagorean theorem:
BD² = AD² +AB² = 1 + 1 = 2
BD = √2 . . . . taking the square root
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We are told that BD = DC, so we know the larger triangle is also an isosceles right triangle. This one has short sides of length √2, so the long side (BC) will have length (√2)×(√2) = 2.
The length of BC is 2 units.