Question

1. 21 mm, 24 mm, 32 mm

Explanation:

Assuming the problem is to check if these three lengths (21 mm, 24 mm, 32 mm) can form a triangle. The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the remaining side.

Step 1: Check the sum of the first two sides

We add the first two lengths: \(21 + 24 = 45\) mm. Now we compare this sum with the third length (32 mm). Since \(45>32\), this inequality holds.

Step 2: Check the sum of the first and third sides

We add the first and the third lengths: \(21 + 32 = 53\) mm. Now we compare this sum with the second length (24 mm). Since \(53>24\), this inequality holds.

Step 3: Check the sum of the second and third sides

We add the second and the third lengths: \(24 + 32 = 56\) mm. Now we compare this sum with the first length (21 mm). Since \(56>21\), this inequality holds.

Since all three triangle inequalities are satisfied, the lengths 21 mm, 24 mm, and 32 mm can form a triangle.

Answer:

The lengths 21 mm, 24 mm, and 32 mm can form a triangle.