Question

the perimeter of square jklm is 48 units. what is the value of (x)?

(j \quad x + 3 \quad k)
(m \quad l)

6
9
12
15

Explanation:

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<reasoning>

Determine the side length of the square

Using the Properties of Rectangles knowledge point, we know that a square is a regular quadrilateral with four equal sides. Let \(s\) represent the side length of square \(JKLM\). The perimeter \(P\) of a square is given by:
\[P = 4s\]

Given that the perimeter is \(48\) units:
\[4s = 48\]
\[s = 12\]

Set up the equation for x

Using the Properties of Rectangles knowledge point, the side length \(JK\) is represented by the expression \(x + 3\). Since all sides of a square are equal, we equate this expression to the calculated side length:
\[x + 3 = 12\]

Solve for x

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} x + 3 &= 12 \\ x &= 12 - 3 \\ x &= 9 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 6</mcq-option>
<mcq-correct>(B) 9</mcq-correct>
<mcq-option>(C) 12</mcq-option>
<mcq-option>(D) 15</mcq-option>
</answer>

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Answer:

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<reasoning>

Determine the side length of the square

Using the Properties of Rectangles knowledge point, we know that a square is a regular quadrilateral with four equal sides. Let \(s\) represent the side length of square \(JKLM\). The perimeter \(P\) of a square is given by:
\[P = 4s\]

Given that the perimeter is \(48\) units:
\[4s = 48\]
\[s = 12\]

Set up the equation for x

Using the Properties of Rectangles knowledge point, the side length \(JK\) is represented by the expression \(x + 3\). Since all sides of a square are equal, we equate this expression to the calculated side length:
\[x + 3 = 12\]

Solve for x

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} x + 3 &= 12 \\ x &= 12 - 3 \\ x &= 9 \end{aligned}$$

\]
</reasoning>

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<mcq-option>(A) 6</mcq-option>
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<mcq-option>(C) 12</mcq-option>
<mcq-option>(D) 15</mcq-option>
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