The height of an isosceles triangle ABC is 15 cm, the length of the base AC is 16 cm. What is the side of this triangle?
| April 27, 2021 | education
Since, by condition, triangle ABC is isosceles, its height BH is also the median of the triangle. Then AH = CH = AC / 2 = 16/2 = 8 cm.
From the right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AH ^ 2 + BH ^ 2 = 8 ^ 2 + 15 ^ 2 = 64 + 225 = 289.
AB = 17 cm.
Since the triangle is isosceles, then AB = BC = 17 cm.
Answer: The length of the side is 17 cm.
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