Triangle ABC – isosceles, BC = 30; find AD.

Given:

DABC – isosceles

AB = AC = 25

BC = 30

AD – height

Find: AD

Solution:

Since DABC is isosceles, the height AD is both a median and a bisector.

Thus, by the property of the median of an isosceles triangle, drawn from apex to a base:

ВD = СD = 30/2 = 15.

If DADВ is rectangular, then by the Pythagorean theorem:

AD ^ 2 + BD ^ 2 = AB ^ 2

AD ^ 2 = AB ^ 2 – BD ^ 2

AD ^ 2 = 25 ^ 2 – 15 ^ 2

AD ^ 2 = (25 – 15) * (25 + 15) = 10 * 40 = 400

AD = 20

Answer: AD = 20.