Explanation:
In an isosceles triangle, the two equal sides are opposite to the two equal angles, and the third side is opposite to the base angle.
Let's draw the triangle and label the height h, the length of the equal sides a, and the length of the base b:
/|\
/ | \
a / | \ a
/ |h \
/____|____\
b
We know that the length of the equal sides is 10 cm, so a = 10 cm.
We also know that the height is 6 cm, so h = 6 cm.
To find the length of the base b, we can use the Pythagorean theorem, which relates the sides of a right triangle:
b^2 = a^2 - h^2
Substituting the given values, we get:
b^2 = 10^2 - 6^2
b^2 = 100 - 36
b^2 = 64
Taking the square root of both sides, we get:
b = 8
Therefore, the length of the third side (the base) is 8 cm.