Question

What is the length of each side of this equilateral triangle? A 2.5 C 15 B5 D 20 7x - 15. one side is 4x, second side is 3x+5, third side is 7x-15

Answer 1

We have the following equilateral triangle:

Since all its sides have to be equal, we have the following equations:

`\begin{gathered} 4x=3x+5 \\ 4x=7x─15 \\ 7x─15=3x+5 \end{gathered}`

Solving for x each one we get:

`\begin{gathered} \text{First equation:} \\ 4x=3x+5 \\ \Rightarrow4x─3x=5 \\ x=5 \\ \text{Second equation:} \\ 4x=7x─15 \\ \Rightarrow15=7x─4x=3x \\ \Rightarrow x=(15)/(3)=5 \\ x=5 \\ \text{Third equation:} \\ 7x─15=3x+5 \\ \Rightarrow7x─3x=5+15=20 \\ \Rightarrow4x=20 \\ \Rightarrow x=(20)/(4)=5 \\ x=5 \end{gathered}`

we can be sure that x=5. Now the sides are:

`\begin{gathered} x=5 \\ 4x=4(5)=20 \\ 7x─15=7(5)─15=35─15=20 \\ 3x+5=3(5)+5=15+5=20 \end{gathered}`

therefore, the sides of the equilateral triangle measure 20 units