Questions: Given that ABCD is a rhombus, what is the value of x? A. 18.25 B. 20.75 C. 30 D. 64 E. 86 F. Cannot be determined

Transcript text: Given that $A B C D$ is a rhombus, what is the value of $x$ ? A. 18.25 B. 20.75 C. 30 D. 64 E. 86 F. Cannot be determined

Solution

Solution Steps

Step 1: Identify the properties of a rhombus

A rhombus is a type of quadrilateral where all four sides are of equal length. Additionally, the diagonals of a rhombus bisect each other at right angles (90 degrees).

Step 2: Set up the equation using the given information

Given that $ABCD$ is a rhombus, we know that all sides are equal. Therefore, we can set up the equation: \[ AB = BC = CD = DA \]

From the diagram, we have: \[ AB = 3x + 7 \] \[ BC = 2x + 17 \]

Step 3: Solve for $x$

Since $AB = BC$, we can set up the equation: \[ 3x + 7 = 2x + 17 \]

Subtract $2x$ from both sides: \[ x + 7 = 17 \]

Subtract 7 from both sides: \[ x = 10 \]

Final Answer

The value of $x$ is $10$.

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