Question

the perimeter of a quadrilateral (four - sided polygon) is 40 inches. the longest side is three times as long as the shortest side. the other two sides are equally long and are 2 inches longer than the shortest side. find the length of all four sides. the length of the shortest side is \boxed{} inches.

Explanation:

Step1: Define variables

Let the length of the shortest side be \( x \) inches. Then the longest side is \( 3x \) inches, and the other two equal sides are \( x + 2 \) inches each.

Step2: Set up perimeter equation

The perimeter of a quadrilateral is the sum of all its sides. So, \( x + 3x + (x + 2) + (x + 2) = 40 \).

Step3: Simplify the equation

Combine like terms: \( x + 3x + x + 2 + x + 2 = 40 \) becomes \( 6x + 4 = 40 \).

Step4: Solve for \( x \)

Subtract 4 from both sides: \( 6x = 40 - 4 = 36 \). Then divide by 6: \( x = \frac{36}{6} = 6 \).

Answer:

6