Equilateral 83013

Traffic signs are equilateral triangles with a side length of 900 mm. How many euros does a galvanized sheet cost to produce 50 pieces of such brands if we consider adding 15% of the material for waste? The price of 1 square meter of sheet metal is 6.5 euros.

Correct answer:

x =  131.09 eur

Step-by-step explanation:

$$\begin{gathered} a=900\text{mm}\to \text{m}=900:1000\text{m}=0.9\text{m} \\ {S}_1=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 0.9^2\doteq 0.3507{\text{m}}^2 \\ n=50 \\ r=100\%+15\%=1+\frac{15}{100}=1.15 \\ {S}_{50}=S_1\cdot n=0.3507\cdot 50\doteq 17.537{\text{m}}^2 \\ {S}_2=r\cdot S_{50}=1.15\cdot 17.537\doteq 20.1676{\text{m}}^2 \\ x=6.5\cdot S_2=6.5\cdot 20.1676=131.09\text{eur} \end{gathered}$$

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