Question

1. the expression 15x + 11 represents the perimeter of the trapezoid. what is the length of the fourth side? explain your reasoning.

(image of trapezoid with sides labeled: 2x + 3, 3x + 4, 4x - 1, and the fourth side unknown)

Explanation:

Step1: Recall Perimeter Formula

The perimeter \( P \) of a trapezoid (or any polygon) is the sum of all its side lengths. Let the four sides be \( 2x + 3 \), \( 3x + 4 \), \( 4x - 1 \), and \( s \) (the unknown side). So, \( P=(2x + 3)+(3x + 4)+(4x - 1)+s \).

Step2: Simplify Known Sides Sum

Combine like terms for the known sides: \( (2x+3x + 4x)+(3 + 4-1)=9x + 6 \).

Step3: Set Up Equation with Perimeter

We know the perimeter \( P = 15x+11 \). So, \( 9x + 6+s=15x + 11 \).

Step4: Solve for \( s \)

Subtract \( 9x + 6 \) from both sides: \( s=(15x + 11)-(9x + 6)=15x-9x+11 - 6 = 6x+5 \).

Answer:

The length of the fourth side is \( 6x + 5 \).