Question

int math 2a pringle adding and subtracting polynomials pablo folds a straw into a triangle with side lengths of 4x^{2}-3 inches, 4x^{2}-2 inches, and 4x^{2}-1 inches. which expression can be used to find the perimeter of the triangle, and what is the perimeter when x = 1.5? 12x^{2}; 36 inches 12x^{2}; 27 inches 12x^{2}-6; 30 inches 12x^{2}-6; 21 inches

Explanation:

Step1: Find perimeter formula

The perimeter $P$ of a triangle is the sum of its side - lengths. Given side - lengths $4x^{2}-3$, $4x^{2}-2$, and $4x^{2}-1$. So $P=(4x^{2}-3)+(4x^{2}-2)+(4x^{2}-1)$.
Combining like terms:
\[

$$\begin{align*} P&=(4x^{2}+4x^{2}+4x^{2})+(-3 - 2-1)\\ &=12x^{2}-6 \end{align*}$$

\]

Step2: Substitute $x = 1.5$

Substitute $x = 1.5$ into the perimeter formula $P = 12x^{2}-6$.
First, calculate $x^{2}=(1.5)^{2}=2.25$.
Then, $12x^{2}=12\times2.25 = 27$.
Finally, $P=12x^{2}-6=27 - 6=21$ inches.

Answer:

$12x^{2}-6;21$ inches