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 $x = 1.5$?
\bigcirc $12x^2 - 6$; 21 inches
\bigcirc $12x^2$; 27 inches
\bigcirc $12x^2 - 6$; 30 inches
\bigcirc $12x^2$; 36 inches

Question

Accepted Answer

# Explanation:
## Step1: Find the perimeter expression
The perimeter $ P $ of a triangle is the sum of its three sides. The sides are $ 4x^2 - 3 $, $ 4x^2 - 2 $, and $ 4x^2 - 1 $. So, we add them together:
$$
\begin{align*}
P&=(4x^2 - 3)+(4x^2 - 2)+(4x^2 - 1)\
&=4x^2+4x^2+4x^2-3 - 2 - 1\
&=12x^2-6
\end{align*}
$$
## Step2: Calculate the perimeter when $ x = 1.5 $
Substitute $ x = 1.5 $ into the expression $ 12x^2-6 $. First, calculate $ x^2=(1.5)^2 = 2.25 $. Then:
$$
\begin{align*}
12x^2-6&=12\times2.25-6\
&=27 - 6\
&=21
\end{align*}
$$
Wait, no, wait. Wait, $ 1.5^2 = 2.25 $, $ 12\times2.25=27 $, $ 27 - 6 = 21 $? But wait, let's check again. Wait, maybe I made a mistake. Wait, $ 4x^2-3 + 4x^2-2 + 4x^2-1=12x^2-6 $. Then when $ x = 1.5 $, $ x^2=(3/2)^2 = 9/4 $. So $ 12\times(9/4)=27 $, $ 27 - 6 = 21 $. But wait, the options have 12x² -6 and 30? Wait, no, maybe I miscalculated. Wait, $ x = 1.5 $, so $ x^2 = 2.25 $, 12*2.25=27, 27 -6=21. But let's check the options. The first option is 12x² -6; 21 inches. Wait, but let's re - check the addition of the constants: -3 -2 -1=-6. So the perimeter expression is 12x² -6. Then when x = 1.5, 12*(1.5)² -6=12*2.25 -6=27 -6=21. So the correct option is the first one? Wait, no, wait the third option is 12x² -6; 30. Wait, maybe I messed up x. Wait, x = 1.5, so x²=2.25, 12*2.25=27, 27 -6=21. So the first option is 12x² -6; 21 inches. But let's check the problem again. Wait, maybe I made a mistake in the sign. Wait, the sides are 4x² -3, 4x² -2, 4x² -1. So adding them: 4x²+4x²+4x²=12x². Then -3 + (-2)+(-1)= -6. So perimeter is 12x² -6. Then x = 1.5, so 12*(1.5)^2 -6=12*2.25 -6=27 -6=21. So the first option is A. 12x² -6; 21 inches. Wait, but let's check the options again. The first option is "12x² -6; 21 inches", the third is "12x² -6; 30 inches". Wait, maybe I made a mistake in x. Wait, x = 2? No, the problem says x = 1.5. Wait, 1.5 is 3/2. Let's compute 12*(3/2)² -6=12*(9/4)-6=27 -6=21. So the correct option is the first one: 12x² -6; 21 inches.
# Answer:
A. $ 12x^2 - 6 $; 21 inches

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QUESTION IMAGE

Question

Explanation:

Step1: Find the perimeter expression

Step2: Calculate the perimeter when \( x = 1.5 \)

Answer: