purple: the perimeter of a triangle is represented by ( 3x^2 + 8x - 9 ). two of its sides are represented by ( (x^2 + 11x + 5) ) and ( (-2x^2 - 4x + 2) ). what expression would represent the third side?

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Accepted Answer

# Explanation:
## Step1: Recall the formula for the perimeter of a triangle
The perimeter $P$ of a triangle with sides $a$, $b$, and $c$ is $P=a + b+ c$. Let $a=x^{2}+11x + 5$, $b=-2x^{2}-4x + 2$, $P = 3x^{2}+8x-9$. We need to find $c$, so $c=P-(a + b)$.
## Step2: Find $a + b$
$$
\begin{align*}
a + b&=(x^{2}+11x + 5)+(-2x^{2}-4x + 2)\
&=x^{2}-2x^{2}+11x-4x+5 + 2\
&=-x^{2}+7x+7
\end{align*}
$$
## Step3: Find $c$
$$
\begin{align*}
c&=(3x^{2}+8x-9)-(-x^{2}+7x+7)\
&=3x^{2}+8x-9 + x^{2}-7x-7\
&=(3x^{2}+x^{2})+(8x-7x)+(-9-7)\
&=4x^{2}+x-16
\end{align*}
$$

# Answer:
$4x^{2}+x - 16$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the perimeter of a triangle

Step2: Find \(a + b\)

Step3: Find \(c\)

Answer: