In triangle ABC, side AB is 13 cm, height BD divides the base of AC into segments AD 5 cm. CD 16 c. Find a BC side?
| January 31, 2021 | education
The height BD divides an arbitrary triangle ABC into two right-angled triangles ABD and CBD. From the Pythagorean theorem we find the height BD.
AB² = BD² + AD²
BD² = 13² – 5²
BD² = 169 – 25
BD² = 144
BD = 12 cm.
Consider the CBD triangle. Also, by the Pythagorean theorem, we find the hypotenuse of BC.
BC² = CD² + BD²
BC² = 16² + 12²
BC² = 256 +144
BC² = 400
BC = 20.
Answer: BC side = 20 cm.
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