Question

With the base of 12x - 4, and side length of 6x + 8 ,what is the perimeter of this equilateral triangle?

Answer 1

Since the triangle is equilateral, then all the sides have the same length. Then:

`12x-4=6x+8`

Solve for x:

`\begin{gathered} \Rightarrow12x-6x=8+4 \\ \Rightarrow6x=12 \\ \Rightarrow x=(12)/(6) \\ \therefore x=2 \end{gathered}`

Substitute x=2 in any of the expressions for the length of a side to find the measure of the side of the triangle:

`6(2)+8=12+8=20`

Since one side has a length of 20 and the triangle has three equal-length sides, then the perimeter is:

`\begin{gathered} P=3\cdot20 \\ =60 \end{gathered}`

Therefore, the perimeter of the equilateral triangle is 60.