To solve this problem, we need to determine which heights could round to the given measurements of 58.63 mm for the rectangle and 73.21 mm for the triangle, when rounded to the nearest hundredth.
First, let's analyze the rounding rules for the nearest hundredth:
- A number will round to 58.63 if it is between 58.625 and 58.635 (58.625 rounds to 58.63 and anything less than 58.625 rounds down to 58.62, while anything greater than or equal to 58.635 rounds up to 58.64).
- Similarly, a number will round to 73.21 if it is between 73.205 and 73.215.
Now let's evaluate each option:
A. 58.635 mm and 73.208 mm
- 58.635 rounds to 58.64 (too high).
- 73.208 falls within 73.205 and 73.215 (correct).
- This pair cannot be correct because 58.635 does not round to 58.63.
B. 58.627 mm and 73.214 mm
- 58.627 rounds to 58.63 (correct).
- 73.214 rounds to 73.21 (correct).
- This pair could be the actual heights measured.
C. 58.624 mm and 73.206 mm
- 58.624 rounds to 58.62 (too low).
- 73.206 rounds to 73.21 (correct).
- This pair cannot be correct because 58.624 does not round to 58.63.
D. 58.633 mm and 73.217 mm
- 58.633 rounds to 58.63 (correct).
- 73.217 rounds to 73.22 (too high).
- This pair cannot be correct because 73.217 does not round to 73.21.
The only option that yields the correct rounded results for both shapes is: B. 58.627 mm and 73.214 mm.