The perimeter of the rectangle below is 118 units. Find the length of side QR.Write your answer without variables.4x+3x3PQRS

1. Break Down the Problem

We are given the perimeter of a rectangle $PQRS$ as 118 units. The sides of the rectangle can be represented as $PQ$ and $QR$, with $PQ$ linked to a variable expression. We need to find the length of side $QR$.

2. Relevant Concepts

The perimeter $P$ of a rectangle can be calculated using the formula: $P = 2 \times (l + w)$ where $l$ is the length and $w$ is the width.

In this case, we can interpret:

• Let $PQ = 4x$
• Let $QR = 3x$

3. Analysis and Detail

Since we need to calculate the perimeter: $P = 2 \times (PQ + QR) = 2 \times (4x + 3x)$ Substituting the perimeter value: $118 = 2 \times (4x + 3x)$ $118 = 2 \times (7x)$ $118 = 14x$ Now, we can solve for $x$: $x = \frac{118}{14} = 8.4286 \, (\text{approximately})$

Now, we find the length of side QR, which is: $QR = 3x = 3 \times 8.4286 = 25.2858 \, (\text{approximately})$ Thus, we can represent $QR$ in more accurate terms.

4. Verify and Summarize

I will summarize both results:

• The calculated value of $x$ is $8.4286$
• The approximate value of side $QR$ is $25.2858$ units.

Final Answer

The length of side $QR$ is approximately 25.29 units.