Question

a scalene triangle is given with side lengths $(2x^{2}+3),(1 + 4x)$ and $(3x^{2}+2)$. select the expression that shows the perimeter of the scalene triangle. a $9x^{3}+6$ b $5x^{2}+4x + 6$ c $5x^{2}+4x + 1$ d $6x^{2}+4x + 6$

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of its side - lengths. So $P=(2x^{2}+3)+(1 + 4x)+(3x^{2}+2)$.

Step2: Combine like - terms

First, combine the $x^{2}$ terms: $2x^{2}+3x^{2}=5x^{2}$. Then, the $x$ term remains as $4x$. Finally, combine the constant terms: $3 + 1+2=6$. So $P = 5x^{2}+4x + 6$.

Answer:

B. $5x^{2}+4x + 6$