If the roof eaves is 0.90 meters wide and simple hip roof is used, how many lineal meters of gutter will be needed?

Steps to Solve

1. Calculate the dimensions of the roof First, determine the dimensions of the roof using the area. The area of the roof is given as 301 square meters. If the roof is a rectangle, we can express the area as: $$ \text{Area} = \text{Length} \times \text{Width} $$ Assuming a simple rectangular shape for the roof, we can set the width to be the same as the eaves (0.90 meters). Thus, we can find the length as: $$ \text{Length} = \frac{\text{Area}}{\text{Width}} = \frac{301 , \text{sqm}}{0.9 , \text{m}} \approx 334.44 , \text{m} $$

2. Determine the perimeter of the roof Next, calculate the perimeter (P) of the roof including the eaves. For a simple hip roof, the perimeter is given by: $$ P = 2 \times (\text{Length} + \text{Width}) $$ Substituting the values: $$ P = 2 \times (334.44 , \text{m} + 0.9 , \text{m}) = 2 \times (335.34 , \text{m}) = 670.68 , \text{m} $$

3. Adjust for the width of the eaves Since we have 0.90 meters of eaves on both sides (which is already accounted in the length), we do not need to modify the perimeter for additional lengths; therefore, we directly use the calculated perimeter.

4. Calculate the total length of gutter needed Finally, we know that the gutter is installed along the perimeter calculated. Therefore, the total length of gutter required is the same as the perimeter of the roof: $$ \text{Length of gutter} = P = 670.68 , \text{m} $$

However, we need the value in lineal meters (lm), so we convert 670.68 m to lineal meters: $$ 670.68 , \text{m} \quad (\text{which is the same as } \text{ln}) $$

5. Select the correct option We compare the calculated length (670.68 lm) with the options provided to find the closest match. The closest option is likely between 53.6 lm, 57.2 lm, 55.4 lm, 51.8 lm. We check if a calculation error has affected the value to ensure it aligns correctly.