Question

of the third mp3 player.

1. the perimeter of a triangle is 42 inches. one side measures 18 inches. the shortest side measures x inches. the longest side measures 1 inch less than four times the length of the shortest side. write and solve an equation to find the length of the longest side.

Explanation:

Step1: Define the sides

Let the shortest side be \( x \) inches. The other side is 18 inches. The longest side is \( 4x - 1 \) inches (since it's 1 inch less than four times the shortest side).

Step2: Write the perimeter equation

The perimeter of a triangle is the sum of its three sides. So, \( x + 18 + (4x - 1) = 42 \).

Step3: Simplify the equation

Combine like terms: \( x + 4x + 18 - 1 = 42 \) → \( 5x + 17 = 42 \).

Step4: Solve for \( x \)

Subtract 17 from both sides: \( 5x = 42 - 17 \) → \( 5x = 25 \). Divide by 5: \( x = 5 \).

Step5: Find the longest side

Substitute \( x = 5 \) into the longest side expression: \( 4(5) - 1 = 20 - 1 = 19 \).

Answer:

The length of the longest side is 19 inches.