Question

if the perimeter of this triangle is 130 cm, form an equation in terms of x and solve for the unknown.

Explanation:

Step1: Sum the sides for perimeter

The perimeter of a triangle is the sum of its three sides. So we add \(4x + 2\), \(9x - 12\), and \(6x + 7\) and set it equal to 130.
\((4x + 2)+(9x - 12)+(6x + 7)=130\)

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms:
\(4x+9x + 6x+2-12 + 7=130\)
\(19x-3 = 130\)

Step3: Solve for \(x\)

Add 3 to both sides:
\(19x-3 + 3=130 + 3\)
\(19x=133\)
Divide both sides by 19:
\(x=\frac{133}{19}\)
\(x = 7\)

Answer:

\(x = 7\)