Question

4 can a triangle have sides with the given lengths? explain. 16. 2 in., 3 in., 6 in. 17. 11 cm, 12 cm, 15 cm 18. 8 m, 10 m, 19 m 19. 1 cm, 15 cm, 15 cm 20. 2 yd, 9 yd, 10 yd 21. 4 m, 5 m, 9 m 5 algebra the lengths of two sides of a triangle are given. describe the lengths possible for the third side. 22. 8 ft, 12 ft 23. 5 in., 16 in. 24. 6 cm, 6 cm

Explanation:

To solve these problems, we use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Problem 16: 2 in., 3 in., 6 in.

Step 1: Check \( 2 + 3 \) vs. \( 6 \)

\( 2 + 3 = 5 \). Since \( 5 < 6 \), the sum of the two shorter sides is not greater than the longest side.

Step 2: Confirm other inequalities (optional, but for completeness)

\( 2 + 6 = 8 > 3 \) and \( 3 + 6 = 9 > 2 \), but the first inequality fails.

Step 1: Check \( 11 + 12 \) vs. \( 15 \)

\( 11 + 12 = 23 > 15 \).

Step 2: Check \( 11 + 15 \) vs. \( 12 \)

\( 11 + 15 = 26 > 12 \).

Step 3: Check \( 12 + 15 \) vs. \( 11 \)

\( 12 + 15 = 27 > 11 \).
All three inequalities hold.

Step 1: Check \( 8 + 10 \) vs. \( 19 \)

\( 8 + 10 = 18 \). Since \( 18 < 19 \), the sum of the two shorter sides is not greater than the longest side.

Step 2: Confirm other inequalities (optional)

\( 8 + 19 = 27 > 10 \) and \( 10 + 19 = 29 > 8 \), but the first inequality fails.

Answer:

No, because \( 2 + 3
ot> 6 \).

Problem 17: 11 cm, 12 cm, 15 cm