Question

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 $10n^{2}-5n$

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. \(3n^{2}\)