The perimeter of an isosceles triangle is 50 cm, and one of its sides is 10 cm. Find the length of the other sides of the triangle
Suppose that the side of the triangle is 10 cm.Since the triangle is isosceles, its second side is also 10 cm.Then the sum of the lengths of the two sides is 10 + 10 = 20 cm, and the length of the third side is 50 – 20 = 30 cm. Since, by the property of a triangle, the sum of its two sides is always greater than the third side, such a triangle cannot exist, which means that 10 cm is the length of the base of the triangle. Then the sum of the two lateral sides is 50 – 10 = 40 cm.Since in an isosceles triangle the sides are equal, the length of each of them is 40/2 = 20 cm.
Answer: the lengths of the sides of the triangle are 10 cm, 20 cm and 20 cm.
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