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

univerkov | May 29, 2021 | education

Since triangle ABC, by condition, is isosceles, then its height BD is also its median and bisector, then triangles ABD and СВD are rectangular, and AD = CD = AC / 2 = 6/2 = 3 cm.

Then, in a right-angled triangle ВСD, according to the Pythagorean theorem, we determine the length of the leg ВD.

ВD ^ 2 = ВС ^ 2 – СD ^ 2 = 7 ^ 2 – 3 ^ 2 = 49 – 9 = 40.

ВM = √40 = 2 * √10 cm.

Answer: The length of the height BD is 2 * √10 cm.

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