Courtyard 2

The castle courtyard has the shape of a rhombus, whose one side is 17.5 m long and the distance between opposite sides is 12 m. They want to pave the courtyard with rectangular tiles. The sides of the tile are 40 cm and 20 cm, one tile weighs 0.6 kg. Calculate how many tiles are needed to pave the courtyard. Can all the tiles be transported at once by a car that carries at most 1.2 tonnes of load?

Result

n =  2625
w=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a=17.5\text{m} \\ h=12\text{m} \\ S=a\cdot h=17.5\cdot 12=210{\text{m}}^2 \\ x=40\text{cm}\to \text{m}=40:100\text{m}=0.4\text{m} \\ y=20\text{cm}\to \text{m}=20:100\text{m}=0.2\text{m} \\ {S}_1=x\cdot y=0.4\cdot 0.2=\frac{2}{25}=0.08{\text{m}}^2 \\ n=\lceil S/S_1\rceil =\lceil 210/0.08\rceil =2625 \end{gathered}$$

$$\begin{gathered} m_1=0.6\text{kg} \\ {m}_2=1.2\text{t}\to \text{kg}=1.2\cdot 1000\text{kg}=1200\text{kg} \\ n=2625 \\ m=n\cdot m_1=2625\cdot 0.6=1575\text{kg} \\ m>m_2 \\ w=0 \end{gathered}$$

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