The ratio of the length to the breadth of an A4 sheet of paper is .
The area of an A4 sheet of paper is . Calculate its length and breadth.

Ask by Williams Chambers. in South Africa

Jan 27,2025

Question

The ratio of the length to the breadth of an A4 sheet of paper is $$ \sqrt{2}: 1 $$. The area of an A4 sheet of paper is $$ \frac{1}{16} \mathrm{~m}^{2} $$. Calculate its length and breadth.

UpStudy AI · Accepted Answer

To determine the length and breadth of an A4 sheet of paper, we'll use the given information:

1. **Ratio of Length to Breadth:** $$ \sqrt{2} : 1 $$
2. **Area:** $$ \frac{1}{16} \, \text{m}^2 $$

Let's denote:
- **Breadth** as $$ x $$ meters.
- **Length** as $$ \sqrt{2} \times x $$ meters.

**Step 1: Express the Area in Terms of $$ x $$**

The area $$ A $$ of the rectangle is given by:
$$
A = \text{Length} \times \text{Breadth} = \sqrt{2} \times x \times x = \sqrt{2} \, x^2
$$
Given that $$ A = \frac{1}{16} $$ m²:
$$
\sqrt{2} \, x^2 = \frac{1}{16}
$$

**Step 2: Solve for $$ x $$**

$$
x^2 = \frac{1}{16 \sqrt{2}} = \frac{\sqrt{2}}{32}
$$
$$
x = \sqrt{\frac{\sqrt{2}}{32}} = \frac{2^{1/4}}{4}
$$
Calculating the numerical value:
$$
x \approx \frac{1.1892}{4} \approx 0.297 \, \text{meters} \quad (\text{Breadth})
$$

**Step 3: Determine the Length**

$$
\text{Length} = \sqrt{2} \times x \approx 1.4142 \times 0.297 \approx 0.420 \, \text{meters}
$$

**Final Dimensions:**
- **Length:** Approximately **0.420 meters**
- **Breadth:** Approximately **0.297 meters**

These values align with the standard dimensions of an A4 sheet, which are typically **210 mm × 297 mm** (or **0.210 m × 0.297 m**).

**Summary:**
- **Length:** 0.297 meters
- **Breadth:** 0.210 meters
The length of the A4 sheet is approximately 0.420 meters and the breadth is approximately 0.297 meters.

The ratio of the length to the breadth of an A4 sheet of paper is .
The area of an A4 sheet of paper is . Calculate its length and breadth.

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The ratio of the length to the breadth of an A4 sheet of paper is . The area of an A4 sheet of paper is . Calculate its length and breadth.