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An electrician plans to install solar panels on a rectangular section of roof with an area of 180m^(2). This width of this section of roof is 7(1)/(5)m across. What is the length of this section of roof? m

An electrician plans to install solar panels on a rectangular section of roof with an area of 180 m2 180 \mathrm{~m}^{2} . This width of this section of roof is 715 m 7 \frac{1}{5} \mathrm{~m} across.\newlineWhat is the length of this section of roof?\newlinem \mathrm{m}

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Full solution

Q. An electrician plans to install solar panels on a rectangular section of roof with an area of 180 m2 180 \mathrm{~m}^{2} . This width of this section of roof is 715 m 7 \frac{1}{5} \mathrm{~m} across.\newlineWhat is the length of this section of roof?\newlinem \mathrm{m}
  1. Calculate Area Formula: To find the length of the rectangular section of the roof, we need to use the formula for the area of a rectangle, which is Area=Length×Width\text{Area} = \text{Length} \times \text{Width}. We are given the area and the width, so we can rearrange the formula to solve for the length: Length=AreaWidth\text{Length} = \frac{\text{Area}}{\text{Width}}.
  2. Convert Width to Improper Fraction: First, we need to convert the mixed number for the width into an improper fraction. The width is given as 7157 \frac{1}{5} meters. To convert it, we multiply the whole number by the denominator of the fraction and add the numerator: (7×5)+1=35+1=36(7 \times 5) + 1 = 35 + 1 = 36. So, the width in improper fraction form is 365\frac{36}{5} meters.
  3. Calculate Length with Area and Width: Now we can calculate the length by dividing the area by the width. The area is 180180 square meters, and the width is 365\frac{36}{5} meters. So, Length = 180÷(365)180 \div \left(\frac{36}{5}\right).
  4. Divide by Fraction to Find Length: To divide by a fraction, we multiply by its reciprocal. So, Length=180×(536)\text{Length} = 180 \times \left(\frac{5}{36}\right). We can simplify this by canceling out common factors before multiplying. Both 180180 and 3636 are divisible by 3636. 180÷36=5180 \div 36 = 5, and 36÷36=136 \div 36 = 1. So, Length=5×(51)\text{Length} = 5 \times \left(\frac{5}{1}\right).
  5. Final Length Calculation: Multiplying 55 by 51\frac{5}{1} gives us the length. Length = 5×5=255 \times 5 = 25 meters.

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