Question

1. d(-2, 3), e(5, 5), f(-4, 10) bonus directions: solve each problem given the information. 12. if △jkl is an equilateral triangle, jk = 13x + 5, kl = 17x - 19, and jl = 8x + 35, find the value of x and the measure of each side.

Explanation:

Step1: Set up equation for equilateral - triangle

In an equilateral triangle, all sides are equal. So, we set \(JK = KL\).
\(13x + 5=17x - 19\)

Step2: Solve for \(x\)

First, move the \(x\) - terms to one side and constants to the other side.
\(19 + 5=17x-13x\)
\(24 = 4x\)
Then, divide both sides by 4.
\(x=\frac{24}{4}=6\)

Step3: Find the length of each side

Substitute \(x = 6\) into the expression for \(JK\) (we could also use \(KL\) or \(JL\)).
\(JK=13x + 5=13\times6 + 5=78 + 5=83\)
\(KL=17x - 19=17\times6-19 = 102-19=83\)
\(JL=8x + 35=8\times6+35=48 + 35=83\)

Answer:

\(x = 6\), and the measure of each side is 83.