The desired leg BC lies opposite the angle 30, therefore, its length is equal to half the length of the hypotenuse AB.
AB = 2 * BC. (1).
By condition, AB + BC = 18 cm. (2).
Let us solve the system of two equations 1 and 2 by the substitution method.
AB = 18 – BC.
18 – BC = 2 * BC.
3 * BC = 18.
BC = 18/3 = 6 cm.
AB = 2 * BC = 2 * 6 = 12 cm.
Answer: The length of the side AB = 12 cm, the length of the side BC = 6 cm.
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