Two sides of an isosceles triangle ABC measure 10 cm and 18 cm. Which of the following could be the measure of the third side?

18 cm

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10 cm

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20 cm

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15 cm

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Solution

The correct options are
A 18 cm
B 10 cm
Given a triangle ABC, sum of two sides of a triangle is always greater than the third side. Here it is said that the triangle is an isosceles triangle. Hence, the third side would be either 10 or 18.
If it is 10:
10 + 10 = 20
20 is greater than the third side 18.
If it is 18:
18 + 18 = 36
36 is greater than the third side 10.
Therefore, the third side can be both 10 and 18.

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