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
$12x^{2}$, 30 inches

Explanation:

Step1: Find the perimeter expression

The perimeter \(P\) of a triangle is the sum of its side lengths.
If the side lengths are \(a = 4x^{2}-3\), \(b = 4x^{2}-2\), and \(c = 4x^{2}-1\), then \(P=a + b + c=(4x^{2}-3)+(4x^{2}-2)+(4x^{2}-1)\).
Combine like - terms: \((4x^{2}+4x^{2}+4x^{2})+(-3 - 2-1)=12x^{2}-6\).

Step2: Substitute \(x = 1.5\) into the perimeter expression

When \(x = 1.5\), we substitute \(x\) into \(P = 12x^{2}-6\).
First, calculate \(x^{2}\): \(x^{2}=(1.5)^{2}=2.25\).
Then, calculate \(12x^{2}\): \(12\times2.25 = 27\).
Finally, calculate \(P\): \(P=12x^{2}-6=27 - 6=21\).

Answer:

\(12x^{2}-6\); \(21\) inches