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.

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.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3