Questions: Given RSTU is a rectangle with RZ = 8 and US = 2x + 6, solve for x.

Given RSTU is a rectangle with RZ = 8 and US = 2x + 6, solve for x.
Transcript text: Given RSTU is a rectangle with RZ $=8$ and $U S=2 x+6$, solve for $x$.
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given a rectangle RSTU with RZ = 8 and US = 2x + 6. We need to solve for x.

Step 2: Identify Relationships in a Rectangle

In a rectangle, the diagonals are equal. Therefore, RZ = US.

Step 3: Set Up the Equation

Since RZ = US, we can set up the equation: \[ 8 = 2x + 6 \]

Step 4: Solve for x

Subtract 6 from both sides: \[ 8 - 6 = 2x \] \[ 2 = 2x \]

Divide both sides by 2: \[ x = 1 \]

Final Answer

\[ x = 1 \]

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