Question

an isosceles triangle has legs with length $4x^{2}+3x + 2$ and base length 2. select all of the expressions that show the perimeter of the triangle. a $2(4x^{2}+3x + 2)$ b $2(4x^{2}+3x + 2)+2$ c $8x^{2}+6x + 6$ d $4x^{2}+3x + 4$ e $8x^{2}+3x + 2$

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of the lengths of its sides. For an isosceles triangle with two equal - length legs of length $l = 4x^{2}+3x + 2$ and base of length $b = 2$, the formula is $P=l + l + b$.

Step2: Substitute side - lengths

Substitute $l = 4x^{2}+3x + 2$ and $b = 2$ into the perimeter formula: $P=(4x^{2}+3x + 2)+(4x^{2}+3x + 2)+2$.

Step3: Simplify the expression

First, combine like - terms. Combine the two terms of $4x^{2}$: $4x^{2}+4x^{2}=8x^{2}$. Combine the two terms of $3x$: $3x+3x = 6x$. Combine the constant terms: $2 + 2+2=6$. So $P = 8x^{2}+6x + 6$. Also, we can write the perimeter as $2(4x^{2}+3x + 2)+2$ since $l + l=2l$.

Answer:

B. $2(4x^{2}+3x + 2)+2$
C. $8x^{2}+6x + 6$