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:

p1=3a=32.4=7.2 S1=ah2=aa2(a/2)22=34a2=2.494 cm2 p=3.5p1=3.57.2=25.2  cm 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=3.52S1=3.522.494=30.55 cm2S = 3.5^2 \cdot S_1 = 3.5^2 \cdot 2.494 = 30.55 \ cm^2

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See also our trigonometric triangle calculator. Pythagorean theorem is the base for the right triangle calculator.

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