1.11 - Mr. Littles is building a triangular sandbox using three boards. He already has 2 boards that measure 9 feet and 12 feet. Select all of the values that could represent the length of the third board of his triangular sandbox.
To find the possible values for the length of the third board in Mr. Littles' triangular sandbox, we can apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's denote the length of the third board as x.
Using the triangle inequality theorem:
9 + 12 > x
21 > x
Therefore, the possible values for the length of the third board (x) are any values greater than 21 feet.
To find the possible values for the length of the third board, we need to determine the range within which it can fall.
In a triangle, the sum of any two sides must be greater than the length of the third side. So, let's calculate the ranges.
If we have two boards measuring 9 feet and 12 feet, we can use the following inequalities:
9 + 12 > Third Board Length
Third Board Length + 9 > 12
Third Board Length + 12 > 9
Simplifying these inequalities, we get:
21 > Third Board Length
Third Board Length > -3
Third Board Length > -3
From this, we can determine that the length of the third board should be greater than -3 feet and less than 21 feet.
Since negative lengths are not possible in this scenario, we can exclude any values below 0. Moreover, a length of 0 is not meaningful, so we can exclude that as well.
Therefore, the possible values for the length of the third board are any positive real numbers between 0 and 21 feet, excluding 0.
34
c^2 = 9^2 + 12^2.
C = 15 Ft. (Rt. triangle).
Possible values: 9, 12, 15Ft.
The 9 and 12 Feet lengths form Isosceles triangles.