Calculate 72624

The perimeter of the ABC triangle is 19.6 cm. The following applies to the lengths of its sides: a: c = 1:2, b: c = 5:6. Calculate the lengths of all sides of the triangle ABC.

Correct answer:

a = 3.6296 cm
b = 7.2593 cm
c = 8.7111 cm

Step-by-step explanation:

o = 19.6 cm a : c = 1 : 2 = 5 : 10 b : c = 5 : 6 = 10 : 12 a : b : c = 5 : 10 : 12 d = \frac{o}{5 + 1 0 + 1 2} = \frac{1 9 . 6}{5 + 1 0 + 1 2} = \frac{9 8}{1 3 5} ≐ 0.7259 cm a = 5 \cdot d = 5 \cdot \frac{9 8}{1 3 5} = \frac{5 \cdot 9 8}{1 3 5} = \frac{4 9 0}{1 3 5} = \frac{9 8}{2 7} cm = 3.6296 cm

b = 10 \cdot d = 10 \cdot \frac{9 8}{1 3 5} = \frac{1 0 \cdot 9 8}{1 3 5} = \frac{9 8 0}{1 3 5} = \frac{1 9 6}{2 7} cm = 7.2593 cm

c = 12 \cdot d = 12 \cdot \frac{9 8}{1 3 5} = \frac{1 2 \cdot 9 8}{1 3 5} = \frac{1 1 7 6}{1 3 5} = \frac{3 9 2}{4 5} ≐ 8.7111 cm Verifying Solution: r_{1} = a / b = \frac{9 8}{2 7} / \frac{1 9 6}{2 7} = \frac{9 8}{2 7} : \frac{1 9 6}{2 7} = \frac{9 8}{2 7} \cdot \frac{2 7}{1 9 6} = \frac{9 8 \cdot 2 7}{2 7 \cdot 1 9 6} = \frac{2 6 4 6}{5 2 9 2} = \frac{1}{2} = 0.5 r_{2} = b / c = \frac{1 9 6}{2 7} / \frac{3 9 2}{4 5} = \frac{1 9 6}{2 7} : \frac{3 9 2}{4 5} = \frac{1 9 6}{2 7} \cdot \frac{4 5}{3 9 2} = \frac{1 9 6 \cdot 4 5}{2 7 \cdot 3 9 2} = \frac{8 8 2 0}{1 0 5 8 4} = \frac{5}{6} ≐ 0.8333 o_{2} = a + b + c = \frac{9 8}{2 7} + \frac{1 9 6}{2 7} + \frac{3 9 2}{4 5} = \frac{4 9 0}{1 3 5} + \frac{9 8 0}{1 3 5} + \frac{1 1 7 6}{1 3 5} = \frac{4 9 0 + 9 8 0 + 1 1 7 6}{1 3 5} = \frac{2 6 4 6}{1 3 5} = \frac{9 8}{5} = 19.6 cm

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