\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}

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**.