Question

kat is painting the edge of a triangular stage prop with reflective orange paint. the lengths of the edges of the triangle are $(3x - 4)$ feet, $(x^{2}-1)$ feet, and $(2x^{2}-15)$ feet. what is the perimeter of the triangle if $x = 4$? 16 feet 40 feet 76 feet 80 feet

Explanation:

Step1: Find the perimeter formula

The perimeter \(P\) of a triangle is the sum of its side lengths. So \(P=(3x - 4)+(x^{2}-1)+(2x^{2}-15)\).
Combine like - terms: \(P=(x^{2}+2x^{2})+3x+(-4 - 1-15)=3x^{2}+3x - 20\).

Step2: Substitute \(x = 4\) into the formula

Substitute \(x = 4\) into \(P = 3x^{2}+3x - 20\).
First, calculate \(3x^{2}\): \(3\times4^{2}=3\times16 = 48\).
Second, calculate \(3x\): \(3\times4=12\).
Then, \(P=48 + 12-20\).
\(P=(48 + 12)-20=60 - 20\).

Answer:

\(40\) feet. So the answer is \(40\) feet.