a right triangle is given with side lengths $(n - 5n^{2})$, $(5n^{2}+2n)$ and a base $(3n^{2}-3n)$. select the expression that shows the perimeter of the right triangle. a $3n^{2}$ b $13n^{2}+2n + 4n$ c $3n^{2}-6n$ d $10n^{2}-5n$

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Accepted Answer

# Explanation:
## Step1: Recall perimeter formula
The perimeter $P$ of a triangle is the sum of the lengths of its sides. If the side - lengths of the triangle are $a$, $b$, and $c$, then $P=a + b + c$. Here, $a=(n - 5n^{2})$, $b=(5n^{2}+2n)$, and $c=(3n^{2}-3n)$.
## Step2: Add the side - lengths
$$
\begin{align*}
P&=(n - 5n^{2})+(5n^{2}+2n)+(3n^{2}-3n)\
&=n - 5n^{2}+5n^{2}+2n+3n^{2}-3n\
&=( - 5n^{2}+5n^{2}+3n^{2})+(n + 2n-3n)\
&=3n^{2}+0\
&=3n^{2}
\end{align*}
$$
# Answer:
A. $3n^{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall perimeter formula

Step2: Add the side - lengths

Answer: