# The lengths of the two sides of an isosceles triangle are 18 cm and 6 cm, and the length

The lengths of the two sides of an isosceles triangle are 18 cm and 6 cm, and the length of the side of the other isosceles triangle is 6 cm. Find the length of the base of the second triangle if you know that the angle at the base of the first triangle is congruent with the angle at the base of the second triangle.

Because the angles at the base are equal, the triangles are similar. The coefficient of similarity is equal to the ratio of the sides:

6: 18 = 6/18 = 1/3.

So the base of the first triangle is 6, then the base of the second will be:

6 * 1/3 = 2 cm.

Answer: the required base length is 2 cm.

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