Question

question 14 (4 points) write and simplify an expression to represent the perimeter of the triangle. you must show all handwritten work to earn full credit. note: it is not drawn to scale.

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. Given side - lengths \(3x\), \(5(2x - 1)\), and \(2x-1\).

Step2: Write the sum expression

\(P=3x + 5(2x - 1)+(2x - 1)\)

Step3: Expand the second term

Using the distributive property \(a(b + c)=ab+ac\), we expand \(5(2x - 1)=10x-5\). So \(P = 3x+10x - 5+2x - 1\).

Step4: Combine like - terms

Combine the \(x\) - terms: \(3x+10x + 2x=(3 + 10+2)x=15x\), and combine the constant terms: \(-5-1=-6\). So \(P = 15x-6\).

Answer:

\(15x - 6\)