Question

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}-6); 21 inches
(12x^{2}); 27 inches
(12x^{2}-6); 30 inches
(12x^{2}); 36 inches

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:

$$
LATEXBLOCK0
$$

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:

$$
LATEXBLOCK1
$$

Wait, no, wait. Wait, \( 12\times2.25 = 27 \), then \( 27-6 = 21 \)? Wait, but let's check again. Wait, \( x = 1.5 \), \( x^2=2.25 \), \( 12\times2.25 = 27 \), then \( 27 - 6=21 \). But wait, let's check the options. The first option is \( 12x^2 - 6 \); 21 inches. But wait, maybe I made a mistake? Wait, no, let's recalculate. Wait, \( 4x^2-3 + 4x^2-2 + 4x^2-1=12x^2-6 \). Then \( x = 1.5 \), \( x^2 = 2.25 \), \( 12\times2.25=27 \), \( 27 - 6 = 21 \). So the expression is \( 12x^2 - 6 \) and the perimeter is 21 inches. Wait, but let's check the options. The first option is \( 12x^2 - 6 \); 21 inches. But wait, maybe I miscalculated? Wait, no, let's do it again. \( x = 1.5 \), so \( x^2 = (3/2)^2=9/4 = 2.25 \). Then \( 12x^2=12\times9/4 = 27 \), then \( 27 - 6 = 21 \). Yes, that's correct.

Wait, but wait, the first option is \( 12x^2 - 6 \); 21 inches. So that's the correct one.

Answer:

A. \( 12x^2 - 6 \); 21 inches