Artemis has six boards cut in various lengths as shown she wants to use three of them to frame a triangular window in her new clubhouse how many unique triangles can Artemis make with the lengths she has

Question:

The sizes of the length of the boards are as follows;

Number of boards with length, 2 ft = 2

Number of boards with length, 6 ft = 2

Number of boards with length, 9 ft = 2.

Answer:

The answer to the question is;

The number of unique triangles Artemis can make with the lengths she has is four.

Step-by-step explanation:

The sizes of the six boards are as follows

2 by 9 ft length boards

2 by 6 ft length boards

2 by 2 ft length boards

Therefore since the sum of the lengths of the other two sides of a triangle must be greater than the third side, we have the following possible unique triangles

9 ft by 9 ft by 6 ft ... (1)

9 ft by 9 ft by 2 ft ... (2)

6 ft by 6 ft by 9 ft ... (3)

6 ft by 6 ft by 2 ft ... (4)

Therefore we have four unique triangles.