# 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.

Result

p =  25.2 cm
S =  30.55 cm2

#### Solution:

$p _1 = 3a = 3 \cdot 2.4 = 7.2 \ \\ S_1 = \dfrac{ a h}{2} = \dfrac{ a \sqrt{ a^2-(a/2)^2} }{2} = \dfrac{ \sqrt{3}}{4}a^2= 2.494 \ cm^2 \ \\ p = 3.5 \cdot p_1 = 3.5 \cdot 7.2 = 25.2 \ \text{ cm }$
$S = 3.5^2 \cdot S_1 = 3.5^2 \cdot 2.494 = 30.55 \ cm^2$

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