Question

Darnell is building a triangular community garden plot. which set of lengths can be used to create the plot perimeter? A. 20 feet, 12 feet, and 34 feet B. 8 feet, 10 feet, and 19 feet C. 5 feet, 8 feet, and 14 feet D. 12, feet, 14 feet, and 20 feet

Answer 1

Darnell is building a triangular community garden plot.

Which set of lengths can be used to create the plot perimeter?

Recall the triangle inequality theorem which states that the sum of any two sides must be greater than the third side.

$\begin{gathered} a+b>c \\ b+c>a_{} \\ a+c>b \end{gathered}$

Let us analyze each of the given options.

Option A:

a = 20 feet

b = 12 feet

c = 34 feet

$\begin{gathered} a+b>c \\ 20+12>34 \\ 32>34\quad (\text{not satified)} \end{gathered}$

Option B:

a = 8 feet

b = 10 feet

c = 19 feet

$\begin{gathered} a+b>c \\ 8+10>19 \\ 18>19\quad (\text{not satisfied)} \end{gathered}$

Option C:

a = 5 feet

b = 8 feet

c = 14 feet

$\begin{gathered} a+b>c \\ 5+8>14 \\ 13>14\quad (\text{not satisfied)} \end{gathered}$

Option D:

a = 12, feet

b = 14 feet

c = 20 feet

$\begin{gathered} a+b>c \\ 12+14>20 \\ 26>20\quad (\text{satisfied)} \\ b+c>a \\ 14+20>12 \\ 24>12\quad (\text{satisfied)} \\ a+c>b \\ 12+20>14 \\ 22>14\quad (\text{satisfied)} \end{gathered}$

As you can see, only option D satisfies the triangle inequality theorem

Therefore, option D is the correct answer.