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, (x² - 1) feet, and (2x² - 15) feet. what is the perimeter of the triangle if x = 4? 16 feet 40 feet 76 feet 80 feet

Explanation:

Step1: Calculate the length of each side

• For the side \(3x - 4\):

Substitute \(x = 4\) into \(3x-4\), we get \(3\times4 - 4=12 - 4 = 8\)

• For the side \(x^{2}-1\):

Substitute \(x = 4\) into \(x^{2}-1\), we get \(4^{2}-1=16 - 1=15\)

• For the side \(2x^{2}-15\):

Substitute \(x = 4\) into \(2x^{2}-15\), we get \(2\times4^{2}-15=2\times16 - 15=32 - 15 = 17\)

Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So \(P=(3x - 4)+(x^{2}-1)+(2x^{2}-15)\).
After substituting \(x = 4\) and calculating each side length (\(8\), \(15\), \(17\)), \(P=8 + 15+17=40\)

Answer:

40 feet