Tiles

The pupils of the building school have to calculate how many roof tiles they will need to cover the roof of the house in the shape of two rectangles measuring 10 x 7.2 m. One roof tile covers a rectangular area of 22 cm x 32 cm. How many tiles will they need if they have to count on 2% waste and overlap?

Final Answer:

n =  2087

Step-by-step explanation:

$$\begin{gathered} a=10\text{m} \\ b=7.2\text{m} \\ m=2 \\ S=m\cdot a\cdot b=2\cdot 10\cdot 7.2=144{\text{m}}^2 \\ x=22\text{cm}\to \text{m}=22:100\text{m}=0.22\text{m} \\ y=32\text{cm}\to \text{m}=32:100\text{m}=0.32\text{m} \\ {S}_1=x\cdot y=0.22\cdot 0.32=\frac{44}{625}=0.0704{\text{m}}^2 \\ q=100\%+2\%=1+\frac{2}{100}=1.02 \\ {n}_1=\frac{S}{S_1}=\frac{144}{0.0704}=\frac{22500}{11}=2045\frac{5}{11}\doteq 2045.4545 \\ {n}_2=q\cdot n_1=1.02\cdot 2045.4545=\frac{22950}{11}=2086\frac{4}{11}\doteq 2086.3636 \\ n=\lceil n_2\rceil =\lceil 2086.3636\rceil =2087 \end{gathered}$$

Try another example