Question

the roof of the house has 2 rectangles measuring 27ft x 52ft each. estimate how many roof tiles you need to put on a new roof if each tile measures 1ft x 1¾ ft. estimated tiles ≈

Explanation:

Step1: Calculate the area of the roof

The area of one rectangle is \(A = l\times w\). For a rectangle with \(l = 27\) ft and \(w = 52\) ft, \(A_1=27\times52=(30 - 3)\times52=30\times52-3\times52 = 1560-156=1404\) square - feet.
Since there are 2 rectangles, the total area of the roof \(A_{roof}=2\times1404 = 2808\) square - feet.

Step2: Calculate the area of one tile

Each tile has dimensions \(1\) ft\(\times1\frac{3}{4}\) ft. Convert \(1\frac{3}{4}\) to an improper fraction: \(1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}\).
The area of one tile \(A_{tile}=1\times\frac{7}{4}=\frac{7}{4}\) square - feet.

Step3: Calculate the number of tiles

The number of tiles \(n=\frac{A_{roof}}{A_{tile}}\). Substitute \(A_{roof}=2808\) and \(A_{tile}=\frac{7}{4}\) into the formula: \(n=\frac{2808}{\frac{7}{4}}=2808\times\frac{4}{7}\).
\(2808\div7 = 401.14\), and \(401.14\times4\approx1600\).

Answer:

\(1600\)