Question

the perimeter of the triangle shown is 30 inches. what is the length of the longest side of the triangle?

Explanation:

Step1: Set up the perimeter equation

The perimeter of a triangle is the sum of its sides. So, \(x+(4x - 8)+(2x+3)=30\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x + 4x+2x)+(-8 + 3)=30\), which gives \(7x-5 = 30\).

Step3: Solve for \(x\)

Add 5 to both sides: \(7x-5 + 5=30 + 5\), so \(7x=35\). Then divide both sides by 7: \(x=\frac{35}{7}=5\).

Step4: Find the lengths of the sides

• First side: \(x = 5\)
• Second side: \(4x-8=4\times5 - 8=20 - 8 = 12\)
• Third side: \(2x + 3=2\times5+3=10 + 3=13\)

Answer:

13 inches