Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.

Correct result:

p =  25.2 cm
S =  30.55 cm²

Solution:

$$\begin{gathered} p_1=3a=3\cdot 2.4=7.2 \\ {S}_1={\displaystyle \frac{ah}{2}}={\displaystyle \frac{a\sqrt{a^2-(a\mathrm{/}2{)}^2}}{2}}={\displaystyle \frac{\sqrt{3}}{4}}{a}^2=2.494c{m}^2 \\ p=3.5\cdot p_1=3.5\cdot 7.2=25.2\text{ cm} \end{gathered}$$

$S=3.5^2\cdot S_1=3.5^2\cdot 2.494=30.55{\text{cm}}^2$

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