Question

1. if △jkl is an equilateral triangle, jk = 13x + 5, kl = 17x - 19, and jl = 8x + 35, find x and the measure of each side.

Explanation:

Step1: Set up equations

Since it's an equilateral triangle, \(JK = KL = JL\). We can set up the equation \(13x + 5=17x - 19\).

Step2: Solve for \(x\)

Subtract \(13x\) from both sides: \(5 = 4x-19\). Then add 19 to both sides: \(4x=24\), so \(x = 6\).

Step3: Find the side - length

Substitute \(x = 6\) into the expression for any side. Let's use \(JK=13x + 5\). Then \(JK=13\times6 + 5=78 + 5=83\). Since it's equilateral, \(KL = JL=83\) too.

Answer:

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