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

Answer:

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

Step-by-step 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)

$\frac{-4x}{-4}=\frac{-36}{-4}$ (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!