Question

julie wants to construct a triangle out of wood to build a sandbox. she is using boards of wood that she found in her garage and their lengths are shown on the right. select all the combinations of boards that would create a triangular sandbox. (select all that apply.) board t 6 ft board r 7 ft board q 11 ft board s 12 ft board v 19 ft

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Test combinations

• For Q (11 ft), R (7 ft), S (12 ft): $11 + 7=18>12$, $11+12 = 23>7$, $7 + 12=19>11$. This combination forms a triangle.
• For Q (11 ft), R (7 ft), T (6 ft): $7+6 = 13>11$, $6 + 11=17>7$, $7+11 = 18>6$. This combination forms a triangle.
• For Q (11 ft), S (12 ft), V (19 ft): $11+12=23>19$, $11 + 19=30>12$, $12+19 = 31>11$. This combination forms a triangle.
• For R (7 ft), S (12 ft), T (6 ft): $7+6=13>12$, $6 + 12=18>7$, $7+12 = 19>6$. This combination forms a triangle.
• For S (12 ft), T (6 ft), V (19 ft): $6+12 = 18<19$. This combination does not form a triangle.
• For R (7 ft), T (6 ft), V (19 ft): $6+7=13<19$. This combination does not form a triangle.

Answer:

Q.R.S, Q.R.T, Q.S.V, S.T.V, V.Q.R