Question

a triangle has sides with lengths of $5x - 1$, $5x - 5$, and $x + 1$. what is the perimeter of the triangle?
a) $11x - 5$
b) $9x - 5$
c) $x + 5$
d) $6x$

Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. If the side lengths are \(a = 5x-1\), \(b = 5x - 5\), and \(c=x + 1\), then \(P=a + b + c\).

Step2: Substitute the side - length expressions into the perimeter formula

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Step3: Combine like terms

• Combine the \(x\) - terms: \(5x+5x+x=(5 + 5+1)x=11x\).
• Combine the constant terms: \(-1-5 + 1=(-1+1)-5=-5\).

So, \(P = 11x-5\).

Answer:

A. \(11x - 5\)