Question

the perimeter of the pentagon below is 67 units. find the length of side $overline{st}$. write your answer without variables.

Explanation:

Step1: Set up perimeter equation

The perimeter of a pentagon is the sum of its side - lengths. So, \(12+(y + 3)+(3y-2)+12 + 2y=67\).

Step2: Combine like - terms

\((12 + 3-2+12)+(y+3y + 2y)=67\), which simplifies to \(25 + 6y=67\).

Step3: Solve for y

Subtract 25 from both sides: \(6y=67 - 25\), so \(6y=42\). Then divide both sides by 6: \(y=\frac{42}{6}=7\).

Step4: Find the length of side \(\overline{ST}\)

The length of side \(\overline{ST}\) is \(2y\). Substitute \(y = 7\) into \(2y\), we get \(2\times7 = 14\).

Answer:

14