Question

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. So $P=x+(2x - 1)+5(2x - 1)$.

Step2: Expand the expression

Expand $5(2x - 1)$ using the distributive property $a(b - c)=ab - ac$. Here $a = 5$, $b=2x$, $c = 1$, so $5(2x - 1)=10x-5$. Then $P=x+(2x - 1)+(10x-5)$.

Step3: Remove parentheses

$P=x + 2x-1+10x - 5$.

Step4: Combine like - terms

Combine the $x$ - terms: $x+2x + 10x=(1 + 2+10)x=13x$, and combine the constant terms: $-1-5=-6$. So $P = 13x-6$.

Answer:

$13x - 6$