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We are given a quadrilateral with four sides:  
- \( PS = 12 \),  
- \( SR = 3y \),  
- \( RQ = y + 3 \),  
- \( PQ = 4y - 1 \).  

The perimeter of the quadrilateral is 78 units. The perimeter can be expressed as the sum of all sides:

\[
PS + SR + RQ + PQ = 78
\]

Substitute the given values into the equation:

\[
12 + 3y + (y + 3) + (4y - 1) = 78
\]

Now simplify the equation:

\[
12 + 3y + y + 3 + 4y - 1 = 78
\]

\[
14 + 8y = 78
\]

Subtract 14 from both sides:

\[
8y = 64
\]

Now, divide by 8:

\[
y = 8
\]

To find the length of side \( QR \), substitute \( y = 8 \) into \( QR = y + 3 \):

\[
QR = 8 + 3 = 11
\]

So, the length of side \( QR \) is **11 units**.

Would you like further explanation or have any other questions? Here are some related questions for further practice:

1. If the perimeter was 100 units, how would the solution change?
2. What is the length of side \( SR \) with \( y = 8 \)?
3. How do we know the shape is a quadrilateral?
4. What happens if the sides were rearranged?
5. How would you solve this if only three sides were given?

**Tip:** Always double-check your arithmetic when combining like terms to ensure accuracy.

The perimeter of the quadrilateral below is 78 units. Find the length of side QR.

Learn how to calculate the length of side QR of a quadrilateral with a perimeter of 78 units. This problem covers algebraic concepts, such as solving linear equations and perimeter calculations. Suitable for students in Grades 8-10.

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