# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/17

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Question 17

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## Exercise 17

### Question

export const metadata = {
    title: "Question 17",
    authors: [{ name: "Nabil Akbarazzima Fatih" }],
    date: "12/26/2025",
};

A rectangle with length <InlineMath math="p" /> and width <InlineMath math="l" /> has an area of <InlineMath math="32" />. If the perimeter of the rectangle is <InlineMath math="6l" />, what is the value of <InlineMath math="p" />?


### Choices

- [ ] $$4$$
- [ ] $$5$$
- [ ] $$6$$
- [ ] $$7$$
- [x] $$8$$

### Answer & Explanation

export const metadata = {
  title: "Solution 17",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

#### Finding the Relation between <InlineMath math="p" /> and <InlineMath math="l" />

Given that the perimeter of the rectangle is <InlineMath math="6l" />. The formula for the perimeter of a rectangle is <InlineMath math="2(p + l)" /> or <InlineMath math="2p + 2l" />. Thus:

<MathContainer>
  <BlockMath math="\begin{aligned} 6l &= 2p + 2l \\ 6l - 2l &= 2p \\ 4l &= 2p \\ 2l &= p \end{aligned}" />
</MathContainer>

#### Finding the Value of <InlineMath math="l" />

Next, it is known that the area of the rectangle is <InlineMath math="32" />. The formula for the area is <InlineMath math="p \times l" />. We substitute <InlineMath math="p = 2l" /> into the area formula:

<MathContainer>
  <BlockMath math="\begin{aligned} \text{Area} &= 32 \\ p \times l &= 32 \\ (2l) \times l &= 32 \\ 2l^2 &= 32 \\ l^2 &= 16 \\ l &= 4 \end{aligned}" />
</MathContainer>

#### Calculating the Value of <InlineMath math="p" />

After obtaining the value <InlineMath math="l = 4" />, we substitute it back into the equation <InlineMath math="p = 2l" />:

<MathContainer>
  <BlockMath math="p = 2(4) = 8" />
</MathContainer>

So, the value of <InlineMath math="p" /> is <InlineMath math="8" />.


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