Similarity coefficient

The similarity ratio of two equilateral triangles is 4.3 (i.e., 43:10). The length of the side of the smaller triangle is 7.5 cm. Calculate the perimeter and area of ​​the larger triangle.

Correct answer:

o₂ =  96.75 cm
S₂ =  450.36 cm²

Step-by-step explanation:

$$\begin{gathered} a=7.5\text{cm} \\ {o}_1=3\cdot a=3\cdot 7.5=\frac{45}{2}=22.5\text{cm} \\ {S}_1=\frac{\sqrt{3}}{4}\cdot a^2=\frac{\sqrt{3}}{4}\cdot 7.5^2\doteq 24.357{\text{cm}}^2 \\ r=43/10=\frac{43}{10}=4.3 \\ {o}_2=r\cdot o_1=4.3\cdot 22.5=96.75\text{cm} \end{gathered}$$

$S_2=r^2\cdot S_1=4.3^2\cdot 24.357=450.36{\text{cm}}^2$

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