Question

this triangle is equilateral. find the value of z. 10z + 4 8z + 14 z = ?

Explanation:

Step1: Recall equilateral triangle property

In an equilateral triangle, all sides are equal. So, the two given side expressions \(10z + 4\) and \(8z + 14\) are equal.

Step2: Set up the equation

Set \(10z + 4 = 8z + 14\).

Step3: Solve for z

Subtract \(8z\) from both sides: \(10z - 8z + 4 = 8z - 8z + 14\), which simplifies to \(2z + 4 = 14\).
Subtract 4 from both sides: \(2z + 4 - 4 = 14 - 4\), so \(2z = 10\).
Divide both sides by 2: \(\frac{2z}{2}=\frac{10}{2}\), giving \(z = 5\).

Answer:

5