In an isosceles triangle ABC AB = BC = 7 cm, and AC = 6 s. Find the height BD of the triangle.

Given:
triangle ABC – isosceles,
AB = BC = 7 centimeters,
AC = 6 centimeters,
BD is the height.
Find the length of the height BD -?
Decision:
Consider an isosceles triangle ABC. The BD height is the median. Then AD = DC = AC: 2 = 6: 2 = 3 centimeters.
Consider a right-angled triangle ABD. By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
AD ^ 2 + BD ^ 2 = AB ^ 2 (we express the legs BD ^ 2 from this equality);
BD ^ 2 = AB ^ 2 – AD ^ 2;
BD ^ 2 = 7 ^ 2 – 3 ^ 2;
BD ^ 2 = 49 – 9;
BD ^ 2 = 40;
ВD = 2√10 centimeters.
Answer: 2√10 centimeters.