Question

4x^{2}+6x + 1
4x^{2}+6x + 1
5x^{2}-2x - 1

Explanation:

1. Explanation:

• Step1: Recall the perimeter formula for a triangle
• The perimeter \(P\) of a triangle is the sum of the lengths of its three - sides. If the side lengths of the triangle are \(a = 4x^{2}+6x + 1\), \(b = 4x^{2}+6x + 1\), and \(c=5x^{2}-2x - 1\), then \(P=a + b + c\).
• Step2: Substitute the side - length expressions into the perimeter formula
• \(P=(4x^{2}+6x + 1)+(4x^{2}+6x + 1)+(5x^{2}-2x - 1)\).
• Step3: Combine like terms
• Combine the \(x^{2}\) terms: \(4x^{2}+4x^{2}+5x^{2}=(4 + 4+5)x^{2}=13x^{2}\).
• Combine the \(x\) terms: \(6x+6x-2x=(6 + 6 - 2)x = 10x\).
• Combine the constant terms: \(1 + 1-1=1\).
• So, \(P = 13x^{2}+10x + 1\).

1. Answer:

\(13x^{2}+10x + 1\)

Answer:

1. Explanation:

• Step1: Recall the perimeter formula for a triangle
• The perimeter \(P\) of a triangle is the sum of the lengths of its three - sides. If the side lengths of the triangle are \(a = 4x^{2}+6x + 1\), \(b = 4x^{2}+6x + 1\), and \(c=5x^{2}-2x - 1\), then \(P=a + b + c\).
• Step2: Substitute the side - length expressions into the perimeter formula
• \(P=(4x^{2}+6x + 1)+(4x^{2}+6x + 1)+(5x^{2}-2x - 1)\).
• Step3: Combine like terms
• Combine the \(x^{2}\) terms: \(4x^{2}+4x^{2}+5x^{2}=(4 + 4+5)x^{2}=13x^{2}\).
• Combine the \(x\) terms: \(6x+6x-2x=(6 + 6 - 2)x = 10x\).
• Combine the constant terms: \(1 + 1-1=1\).
• So, \(P = 13x^{2}+10x + 1\).

1. Answer:

\(13x^{2}+10x + 1\)