# The perimeter of the triangle is 18 cm, and its sides are in the ratio 2: 3: 4, find the largest angle

October 4, 2021 | education

| The perimeter of a triangle is found by the formula P = a + b + c. Let’s substitute the known data into equality, taking into account the aspect ratio:

2x + 3x + 4x = 18;

5x + 4x = 18;

9x = 18;

x = 18: 9;

x = 2.

Then a = 2x = 2 * 2 = 4 cm, b = 3x = 3 * 2 = 6 cm, c = 4x = 4 * 2 = 8 cm.

Knowing these values, we find the largest angle that lies against the larger side.

Cosine theorem: 4, 6, 8

82 = 42 + 62 – 2 * 4 * 6 * cos a;

64 = 16 + 36 – 48 * cos a;

64 = 52 – 48 * cos a;

64 – 52 = – 48 * cos a;

12 = – 48 * cos a;

cos a = – 12/48 = – 3/12 = – 1/4.

Using the table of values, we find the angle value – 105 °.

Answer: 105 °.

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