This school building is 37 years old.
This is a 37-year-old school building.
The boy is 13 years old.
He is a 13-year-old boy.
The is 170 cm tall.
He is a 170 cm-tall boy.
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Is each pair the same and grammatical?
Yes they are all the same and grammatical -- except the last one should be:
The boy is 170 cm tall.
He is a 170-cm-tall boy.