\begin{tabular}{l} An electrician plans to install solar panels on a rectangular section of roof \ with an area of $$ 180 \mathrm{~m}^{2} $$. This width of this section of roof is $$ 7 \frac{1}{5} $$ m across, \ What is the length of this section of roof? \ Related content \ \hline Dividing whole numbers \& fractions: $$ t $$-shirts \ 29s \end{tabular}

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UpStudy AI · Accepted Answer

To determine the length of the rectangular section of the roof where the electrician plans to install solar panels, we'll use the formula for the area of a rectangle:

$$
\text{Area} = \text{Length} \times \text{Width}
$$

**Given:**
- **Area ($$ A $$)** = $$ 180 \, \mathrm{m}^2 $$
- **Width ($$ W $$)** = $$ 7 \frac{1}{5} \, \mathrm{m} $$

**Step 1: Convert the Mixed Number to an Improper Fraction**

First, convert the mixed number $$ 7 \frac{1}{5} $$ meters into an improper fraction to simplify calculations.

$$
7 \frac{1}{5} = \frac{7 \times 5 + 1}{5} = \frac{35 + 1}{5} = \frac{36}{5} \, \mathrm{m}
$$

**Step 2: Rearrange the Area Formula to Solve for Length**

Rearrange the area formula to solve for the length ($$ L $$):

$$
L = \frac{A}{W}
$$

**Step 3: Substitute the Known Values**

$$
L = \frac{180 \, \mathrm{m}^2}{\frac{36}{5} \, \mathrm{m}} = 180 \times \frac{5}{36}
$$

**Step 4: Simplify the Calculation**

$$
L = 180 \times \frac{5}{36} = \left( \frac{180}{36} \right) \times 5 = 5 \times 5 = 25 \, \mathrm{m}
$$

**Conclusion:**

The length of the rectangular section of the roof is **25 meters**.
The length of the roof section is 25 meters.

An electrician plans to install solar panels on a rectangular section of roof

with an area of . This width of this section of roof is m across,

What is the length of this section of roof?

Related content

Dividing whole numbers & fractions: -shirts

29s

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An electrician plans to install solar panels on a rectangular section of roof with an area of . This width of this section of roof is m across, What is the length of this section of roof? Related content Dividing whole numbers & fractions: -shirts 29s