In triangle ABC AB = 10cm, BC = 17cm, AC = 21cm. Find height BD
| June 11, 2021 | education
We calculate the area of a triangle in two ways, the first, according to Heron’s theorem, and the second, through the height and base.
From the second formula, we determine the height of the triangle.
p = (AB + BC + AC) / 2 = (10 + 17 + 21) / 2 = 24 cm.
Savs = √p * (p – AB) * (p – BC) * (p – AC) = √24 * (24 – 10) * (24 – 17) * (24 – 21) = √24 * 14 * 7 * 3 = √7056 = 84 cm2.
Sас = АС * ВD / 2.
ВD = 2 * Saс / АС = 2 * 84/21 = 8 cm.
Answer: The length of the height BD is 8 cm.
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