Question

If ΔABC is an equilateral triangle with, AB = 2x + 17, BC = 6x - 19, AC = 4x-1, find x and the measure of each side

Answer 1

`x=9, AB=BC=AC=35`

Explanation:

Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that
`AB=BC=AC`. We are given the lengths of all 3 sides in terms of
`x`, but we only need to set two of them equal to each other to solve for
`x`. Let's use
`AB` and
`BC` to solve for
`x`. We know that
`AB=BC`,
`AB=2x+17`, and
`BC=6x-19`. Therefore, we can write the following equation to solve for

`AB=BC\\2x+17=6x-19` (Substitute given values into equation)

Solving for
`x`, we get:

`2x+17=6x-19\\2x+17-17=6x-19-17` (Subtract
`17` from both sides of the equation to isolate constants)

`2x=6x-36` (Simplify)

`2x-6x=6x-36-6x` (Subtract
`6x` from both sides of the equation to isolate
`x`)

`-4x=-36` (Simplify)

`(-4x)/(-4)=(-36)/(-4)` (Divide both sides of the equation by
`-4` to get rid of
`x`'s coefficient)

`x=9` (Simplify)

Therefore,
`AB=2x+17=2*9+17=18+17=35`, and
`AB=BC=AC=35`. Hope this helps!